Residual strain, a tensor quantity, is a critical material property that impacts the overall performance of metal parts. Neutron Bragg edge strain tomography is a technique for imaging residual strain that works by making conventional hyperspectral computed tomography measurements, extracting the average projected strain at each detector pixel, and processing the resulting strain sinogram using a reconstruction algorithm. However, the reconstruction is severely ill-posed as the underlying inverse problem involves inferring a tensor at each voxel from scalar sinogram data.In this paper, we introduce the model-oriented neutron strain tomographic reconstruction (MONSTR) algorithm that reconstructs the 2D residual strain tensor from the neutron Bragg edge strain measurements. MONSTR is based on using the multi-agent consensus equilibrium framework for the tensor tomographic reconstruction. Specifically, we formulate the reconstruction as a consensus solution of a collection of agents representing detector physics, the tomographic reconstruction process, and physics-based constraints from continuum mechanics. Using simulated data, we demonstrate high-quality reconstruction of the strain tensor even when using very few measurements.

Ptychography uses overlapping X-ray diffraction measurements to perform nanometer-scale imaging of objects. Practical illumination sources for ptychography, such as synchrotrons, are not fully coherent, so they exhibit multiple modes. To address this, blind multi-mode ptychography algorithms have been developed that jointly estimate the image along with the multiple probe modes. However, commonly used algorithms, such as DM and SHARP, use a single global estimate of the probe state that does not allow for local spatial variation in the probe.In this paper, we compare a distributed probe state version of the BM-PMACE algorithm to a global probe state version of BM-PMACE as well as to DM and SHARP. Importantly, distributed state BM-PMACE maintains a location-specific probe state that captures spatially varying probe aberrations. Using measured data, we demonstrate that the distributed probe state improves both convergence speed and final image quality compared to the global state algorithms.

X-ray computed tomography (CT) reconstructs the internal morphology of a three dimensional object from a collection of projection images, most commonly using a single rotation axis. However, for objects containing dense materials like metal, the use of a single rotation axis may leave some regions of the object obscured by the metal, even though projections from other rotation axes (or poses) might contain complementary information that would better resolve these obscured regions. In this paper, we propose pixel-weighted Multi-pose Fusion to reduce metal artifacts by fusing the information from complementary measurement poses into a single reconstruction. Our method uses Multi-Agent Consensus Equilibrium (MACE), an extension of Plug-and-Play, as a framework for integrating projection data from different poses. A primary novelty of the proposed method is that the output of different MACE agents are fused in a pixel-weighted manner to minimize the effects of metal throughout the reconstruction. Using real CT data on an object with and without metal inserts, we demonstrate that the proposed pixel-weighted Multi-pose Fusion method significantly reduces metal artifacts relative to single-pose reconstructions.

Neutron computed tomography (nCT) is a 3D char-acterization technique used to image the internal morphology or chemical composition of samples in biology and materials sciences. A typical workflow involves placing the sample in the path of a neutron beam, acquiring projection data at a predefined set of orientations, and processing the resulting data using an analytic reconstruction algorithm. Typical nCT scans require hours to days to complete and are then processed using conventional filtered back-projection (FBP), which performs poorly with sparse views or noisy data. Hence, the main methods in order to reduce overall acquisition time are the use of an improved sampling strategy combined with the use of advanced reconstruction methods such as model-based iterative reconstruction (MBIR). In this paper, we propose an adaptive orientation selection method in which an MBIR reconstruction on previously-acquired measurements is used to define an objective function on orientations that balances a data-fitting term promoting edge alignment and a regularization term promoting orientation diversity. Using simulated and experimental data, we demonstrate that our method produces high-quality reconstructions using significantly fewer total measurements than the conventional approach.

Non-destructive characterization of multi-layered structures that can be accessed from only a single side is important for applications such as well-bore integrity inspection. Existing methods related to Synthetic Aperture Focusing Technique (SAFT) rapidly produce acceptable results but with significant artifacts. Recently, ultrasound model-based iterative reconstruction (UMBIR) approaches have shown significant improvements over SAFT. However, even these methods produce ringing artifacts due to the high fractional-bandwidth of the excitation signal.In this paper, we propose a ringing artifact reduction method for ultrasound image reconstruction that uses a multi-agent consensus equilibrium (RARE-MACE) framework. Our approach integrates a physics-based forward model that accounts for the propagation of a collimated ultrasonic beam in multi-layered media, a spatially varying image prior, and a denoiser designed to suppress the ringing artifacts that are characteristic of reconstructions from high-fractional bandwidth ultrasound sensor data. We test our method on simulated and experimental measurements and show substantial improvements in image quality compared to SAFT and UMBIR.

Hyperspectral neutron tomography is an effective method for analyzing crystalline material samples with complex compositions in a non-destructive manner. Since the counts in the hyperspectral neutron radiographs directly depend on the neutron cross-sections, materials may exhibit contrasting neutron responses across wavelengths. Therefore, it is possible to extract the unique signatures associated with each material and use them to separate the crystalline phases simultaneously.We introduce an autonomous material decomposition (AMD) algorithm to automatically characterize and localize polycrystalline structures using Bragg edges with contrasting neutron responses from hyperspectral data. The algorithm estimates the linear attenuation coefficient spectra from the measured radiographs and then uses these spectra to perform polycrystalline material decomposition and reconstructs 3D material volumes to localize materials in the spatial domain. Our results demonstrate that the method can accurately estimate both the linear attenuation coefficient spectra and associated reconstructions on both simulated and experimental neutron data.

As computational tools for X-ray computed tomography (CT) become more quantitatively accurate, knowledge of the source-detector spectral response is critical for quantitative system-independent reconstruction and material characterization capabilities. Directly measuring the spectral response of a CT system is hard, which motivates spectral estimation using transmission data obtained from a collection of known homogeneous objects. However, the associated inverse problem is ill-conditioned, making accurate estimation of the spectrum challenging, particularly in the absence of a close initial guess.In this paper, we describe a dictionary-based spectral estimation method that yields accurate results without the need for any initial estimate of the spectral response. Our method utilizes a MAP estimation framework that combines a physics-based forward model along with an L0sparsity constraint and a simplex constraint on the dictionary coefficients. Our method uses a greedy support selection method and a new pair-wise iterated coordinate descent method to compute the above estimate. We demonstrate that our dictionary-based method outperforms a state-of-the-art method as shown in a cross-validation experiment on four real datasets collected at beamline 8.3.2 of the Advanced Light Source (ALS).

Collimated beam ultrasound systems are a novel technology for imaging inside multi-layered structures such as geothermal wells. Such systems include a transmitter and multiple receivers to capture reflected signals. Common algorithms for ultrasound reconstruction use delay-and-sum (DAS) approaches; these have low computational complexity but produce inaccurate images in the presence of complex structures and specialized geometries such as collimated beams.In this paper, we propose a multi-layer, ultrasonic, model-based iterative reconstruction algorithm designed for collimated beam systems. We introduce a physics-based forward model to accurately ac-count for the propagation of a collimated ultrasonic beam in multi-layer media and describe an efficient implementation using binary search. We model direct arrival signals, detector noise, and a spatially varying image prior, then cast the reconstruction as a maximum a posteriori estimation problem. Using simulated and experimental data we obtain significantly fewer artifacts relative to DAS while running in near real time using commodity compute resources.

There is growing interest in employing deep neural networks (DNN) for image sharpening. However, sharpening medical computed tomography (CT) images is challenging because sharpening substantially amplifies high-frequency noise. Alternatively, sharpening algorithms that are also designed to denoise produce images lacking texture. Most importantly, radiologists strongly prefer reading images at a consistent level of noise. Hence it is preferable that a sharpening algorithm not substantially change the noise energy or texture.In this work, we propose a noise preserving sharpening filter (NPSF) to sharpen CT images while keeping the noise energy and texture in the result similar to that of the input. We achieve this by adding appropriately scaled noise while training. Furthermore, the NPSF is characterized by three user-adjustable parameters which give flexibility to achieve a desired level of sharpness and noise. Our experiments show that the NPSF can sharpen noisy images while producing desired noise level and texture.

There is growing interest in the use of deep neural network (DNN) based image denoising to reduce patient’s X-ray dosage in medical computed tomography (CT). An effective denoiser must remove noise while maintaining the texture and detail. Commonly used mean squared error (MSE) loss functions in the DNN training weight errors due to bias and variance equally. However, the error due to bias is often more egregious since it results in loss of image texture and detail. In this paper, we present a novel approach to designing a loss function that penalizes variance and bias differently. Our proposed bias-reducing loss function allows us to train a DNN denoiser so that the amount of texture and detail retained can be controlled through a user adjustable parameter. Our experiments verify that the proposed loss function enhances the texture and detail in denoised images with only a slight increase in the MSE.

Energy resolved neutron imaging (ERNI) is an advanced neutron radiography technique capable of non-destructively extracting spatial isotopic information within a given material. Energy-dependent radiography image sequences can be created by utilizing neutron time-of-flight techniques. In combination with uniquely characteristic isotopic neutron cross-section spectra, isotopic areal densities can be determined on a per-pixel basis, thus resulting in a set of areal density images for each isotope present in the sample. By preforming ERNI measurements over several rotational views, an isotope decomposed D computed tomograpy is possible.We demonstrate a method involving a robust and automated background estimation based on a linear programming formulation. The extremely high noise due to low count measurements is overcome using a sparse coding approach. It allows for a significant computation time improvement, from weeks to a few hours compared to existing neutron evaluation tools, enabling at the present stage a semi-quantitative, user-friendly routine application.

There is an increasing need to reconstruct objects in four or more dimensions corresponding to space, time and other independent parameters. The best 4D reconstruction algorithms use regularized iterative reconstruction approaches such as model based iterative reconstruction (MBIR), which depends critically on the quality of the prior modeling. Recently, Plug-and-Play methods have been shown to be an effective way to incorporate advanced prior models using state-of-the-art denoising algorithms designed to remove additive white Gaussian noise (AWGN). However, state-of-the-art denoising algorithms such as BM4D and deep convolutional neural networks (CNNs) are primarily available for 2D and sometimes 3D images. In particular, CNNs are difficult and computationally expensive to implement in four or more dimensions, and training may be impossible if there is no associated high-dimensional training data.In this paper, we present Multi-Slice Fusion, a novel algorithm for 4D and higher-dimensional reconstruction, based on the fusion of multiple low-dimensional denoisers. Our approach uses multi-agent consensus equilibrium (MACE), an extension of Plug-and-Play, as a framework for integrating the multiple lower-dimensional prior models. We apply our method to the problem of 4D cone-beam X-ray CT reconstruction for Non Destructive Evaluation (NDE) of moving parts. This is done by solving the MACE equations using lower-dimensional CNN denoisers implemented in parallel on a heterogeneous cluster. Results on experimental CT data demonstrate that Multi-Slice Fusion can substantially improve the quality of reconstructions relative to traditional 4D priors, while also being practical to implement and train.

Computed tomography (CT) image reconstruction is a crucial technique for many imaging applications. Among various reconstruction methods, Model-Based Iterative Reconstruction (MBIR) enables super-resolution with superior image quality. MBIR, however, has a high memory requirement that limits the achievable image resolution, and the parallelization for MBIR suffers from limited scalability. In this paper, we propose Asynchronous Consensus MBIR (AC-MBIR) that uses Consensus Equilibrium (CE) to provide a super-resolution algorithm with a small memory footprint, low communication overhead and a high scalability. Super-resolution experiments show that AC-MBIR has a 6.8 times smaller memory footprint and 16 times more scalability, compared with the state-of-the-art MBIR implementation, and maintains a 100% strong scaling efficiency at 146880 cores. In addition, AC-MBIR achieves an average bandwidth of 3.5 petabytes per second at 587520 cores.

High-attenuation materials pose significant challenges to computed tomographic imaging. Formed of high mass-density and high atomic number elements, they cause more severe beam hardening and scattering artifacts than do water-like materials. Pre-corrected line-integral density measurements are no longer linearly proportional to the path lengths, leading to reconstructed image suffering from streaking artifacts extending from metal, often along highest-density directions. In this paper, a novel prior-based iterative approach is proposed to reduce metal artifacts. It combines the superiority of statistical methods with the benefits of sinogram completion methods to estimate and correct metal-induced biases. Preliminary results show minimized residual artifacts and significantly improved image quality.

Model-Based Iterative Reconstruction (MBIR) has shown promising results in clinical studies as they allow significant dose reduction during CT scans while maintaining the diagnostic image quality. MBIR improves the image quality over analytical reconstruction by modeling both the sensor (e.g., forward model) and the image being reconstructed (e.g., prior model). While the forward model is typically based on the physics of the sensor, accurate prior modeling remains a challenging problem. Markov Random Field (MRF) has been widely used as prior models in MBIR due to simple structure, but they cannot completely capture the subtle characteristics of complex images. To tackle this challenge, we generate a prior model by learning the desirable image property from a large dataset. Toward this, we use Plug-and-Play (PnP) framework which decouples the forward model and the prior model in the optimization procedure, replacing the prior model optimization by a image denoising operator. Then, we adopt the state-of-the-art deep residual learning for the image denoising operator which represents the prior model in MBIR. Experimental results on real CT scans demonstrate that our PnP MBIR with deep residual learning prior significantly reduces the noise and artifacts compared to analytical reconstruction and standard MBIR with MRF prior.

Model based methods have gained popularity in the past few decades in reconstruction problems particularly when the measurement data is sparse. In model based inference, apart from a model for the measurements, there exists a model for the unknown signal to be reconstructed, called the prior model. Model based methods tend to do very well when the prior model is accurate and representative of real world behavior of the unknown signal. Often these priors are trained from some training data, and therefore, the accuracy of the reconstructions depends inherently on the accuracy of the training data. The reconstructions can come out to be highly biased if the training data is not representative of the actual signal. In this paper, we propose a new hybrid prior model that combines a Markov Random Field model with a Gaussian model trained from a sparse training set. We combine the models using a mixing coefficient Υ E [0, 1], that controls the influence of each of the models. Our main contribution is in the way we combine the two models to produce a whole continuum of prior models for different values of Y where Y can be tuned according to how trustworthy the training set is. Reconstruction results show that our hybrid prior models produces high quality reconstructions even when the training data is not representative.

Regularized inversion methods for image reconstruction are used widely due to their tractability and their ability to combine complex physical sensor models with useful regularity criteria. Such methods motivated the recently developed Plug-and-Play prior method, which provides a framework to use advanced denoising algorithms as regularizers in inversion. However, the need to formulate regularized inversion as the solution to an optimization problem limits the expressiveness of possible regularity conditions and physical sensor models. In this paper, we introduce the idea of consensus equilibrium (CE), which generalizes regularized inversion to include a much wider variety of both forward (or data fidelity) components and prior (or regularity) components without the need for either to be expressed using a cost function. CE is based on the solution of a set of equilibrium equations that balance data fit and regularity. In this framework, the problem of MAP estimation in regularized inversion is replaced by the problem of solving these equilibrium equations, which can be approached in multiple ways. The key contribution of CE is to provide a novel framework for fusing multiple heterogeneous models of physical sensors or models learned from data. We describe the derivation of the CE equations and prove that the solution of the CE equations generalizes the standard MAP estimate under appropriate circumstances. We also discuss algorithms for solving the CE equations, including a version of the Douglas--Rachford/alternating direction method of multipliers algorithm with a novel form of preconditioning and Newton's method, both standard form and a Jacobian-free form using Krylov subspaces. We give several examples to illustrate the idea of CE and the convergence properties of these algorithms and demonstrate this method on some toy problems and on a denoising example in which we use an array of convolutional neural network denoisers, none of which is tuned to match the noise level in a noisy image but which in consensus can achieve a better result than any of them individually.

The inherent noise in the observed (e.g., scanned) binary document image degrades the image quality and harms the compression ratio through breaking the pattern repentance and adding entropy to the document images. In this paper, we design a cost function in Bayesian framework with dictionary learning. Minimizing our cost function produces a restored image which has better quality than that of the observed noisy image, and a dictionary for representing and encoding the image. After the restoration, we use this dictionary (from the same cost function) to encode the restored image following the symbol-dictionary framework by JBIG2 standard with the lossless mode. Experimental results with a variety of document images demonstrate that our method improves the image quality compared with the observed image, and simultaneously improves the compression ratio. For the test images with synthetic noise, our method reduces the number of flipped pixels by 48.2% and improves the compression ratio by 36.36% as compared with the best encoding methods. For the test images with real noise, our method visually improves the image quality, and outperforms the cutting-edge method by 28.27% in terms of the compression ratio.

Computed Tomography (CT) Image Reconstruction is an important technique used in a variety of domains, including medical imaging, electron microscopy, non-destructive testing and transportation security. Model-based Iterative Reconstruction (MBIR) using Iterative Coordinate Descent (ICD) is a CT algorithm that produces state-of-the-art results in terms of image quality. However, MBIR is highly computationally intensive and challenging to parallelize, and has traditionally been viewed as impractical in applications where reconstruction time is critical. We present the first GPU-based algorithm for ICD-based MBIR. The algorithm leverages the recently-proposed concept of SuperVoxels, and efficiently exploits the three levels of parallelism available in MBIR to better utilize the GPU hardware resources. We also explore data layout transformations to obtain more coalesced accesses and several GPU-specific optimizations for MBIR that boost performance. Across a suite of 3200 test cases, our GPU implementation obtains a geometric mean speedup of 4.43X over a state-of-the-art multi-core implementation on a 16-core iso-power CPU.

Computed Tomographic (CT) image reconstruction is an important technique used in a wide range of applications. Among reconstruction methods, Model-Based Iterative Reconstruction (MBIR) is known to produce much higher quality CT images; however, the high computational requirements of MBIR greatly restrict their application. Currently, MBIR speed is primarily limited by irregular data access patterns, the difficulty of effective parallelization, and slow algorithmic convergence.

An increasing number of X-ray CT procedures are being conducted with drastically reduced dosage, due at least in part to advances in statistical reconstruction methods that can deal more effectively with noise than can traditional techniques. As data become photon-limited, more detailed models are necessary to deal with count rates that drop to the levels of system electronic noise. We present two options for sinogram pre-treatment that can improve the performance of photon-starved measurements, with the intent of following with model-based image reconstruction. Both the local linear minimum mean-squared error (LLMMSE) filter and pointwise Bayesian restoration (PBR) show promise in extracting useful, quantitative information from very low-count data by reducing local bias while maintaining the lower noise variance of statistical methods. Results from clinical data demonstrate the potential of both techniques.

Model based iterative reconstruction (MBIR) algorithms have been used to greatly improve image quality and temporal resolution in synchrotron based time-space Computed Tomography (CT). Among the various optimization methods that have been used for MBIR, iterative coordinate descent (ICD) has relatively lower computational requirements because it converges fast. In spite of that, long execution time remains a barrier for the widespread use of MBIR. In this paper, we present a new data structure, called VL-Buffer, for time-space reconstruction that significantly improves the cache locality while retaining good parallel performance. Experimental results show an average speedup of 40% using VL-Buffer.

X-ray propagation-based phase contrast tomography (XPCT) has become popular as a method for tomographically reconstructing the complex refractive index of a material from single distance measurements. XPCT has two major advantages over traditional X-ray computed tomography (CT): It can be used at higher cone-beam magnifications, and it typically produces higher contrast. However, current XPCT reconstruction algorithms are limited to near-field diffraction, which limits both their use and the quality of reconstructions. In this paper, we present a model-based iterative reconstruction (MBIR) algorithm called complex refractive index tomographic iterative reconstruction (CRITIR). CRITIR is based on a non-linear physics based model for X-ray propagation and a prior model for the complex refractive index of the object being imaged. Unlike conventional methods, CRITIR is designed to work within and beyond the near-field diffraction region. We use simulation to show that our algorithm accurately reconstructs the object while the conventional methods result in inaccurate reconstructions with blurry edges beyond the near-field region.

Computed tomography is increasingly enabling scientists to study physical processes of materials at micron scales. The MBIR framework provides a powerful method for CT reconstruction by incorporating both a measurement model and prior model. Classically, the choice of prior has been limited to models enforcing local similarity in the image data. In some material science problems, however, much more may be known about the underlying physical process being imaged. Moreover, recent work in Plug-And-Play decoupling of the MBIR problem has enabled researchers to look beyond classical prior models, and innovations in methods of data acquisition such as interlaced view sampling have also shown promise for imaging of dynamic physical processes. In this paper, we propose an MBIR framework with a physics based prior model - namely the Cahn-Hilliard equation. The Cahn-Hilliard equation can be used to describe the spatiotemporal evolution of binary alloys. After formulating the MBIR cost with Cahn-Hilliard prior, we use Plug-And-Play algorithm with ICD optimization to minimize this cost. We apply this method to simulated data using the interlaced-view sampling method of data acquisition. Results show superior reconstruction quality compared to the Filtered Back Projection. Though we use Cahn-Hilliard equation as one instance, the method can be easily extended to use any other physics-based prior model for a different set of applications.

Despite the recent flight control regulations, Unmanned Aerial Vehicles (UAVs) are still gaining popularity in civilian and military applications, as much as for personal use. Such emerging interest is pushing the development of effective collision avoidance systems. Such systems play a critical role UAVs operations especially in a crowded airspace setting. Because of cost and weight limitations associated with UAVs payload, camera based technologies are the de-facto choice for collision avoidance navigation systems. This requires multi-target detection and tracking algorithms from a video, which can be run on board efficiently. While there has been a great deal of research on object detection and tracking from a stationary camera, few have attempted to detect and track small UAVs from a moving camera. In this paper, we present a new approach to detect and track UAVs from a single camera mounted on a different UAV. Initially, we estimate background motions via a perspective transformation model and then identify distinctive points in the background subtracted image. We find spatio-temporal traits of each moving object through optical flow matching and then classify those candidate targets based on their motion patterns compared with the background. The performance is boosted through Kalman filter tracking. This results in temporal consistency among the candidate detections. The algorithm was validated on video datasets taken from a UAV. Results show that our algorithm can effectively detect and track small UAVs with limited computing resources.

Computed Tomography (CT) Image Reconstruction is an important technique used in a wide range of applications, ranging from explosive detection, medical imaging to scientific imaging. Among available reconstruction methods, Model Based Iterative Reconstruction (MBIR) produces higher quality images and allows for the use of more general CT scanner geometries than is possible with more commonly used methods. The high computational cost of MBIR, however, often makes it impractical in applications for which it would otherwise be ideal. This paper describes a new MBIR implementation that significantly reduces the computational cost of MBIR while retaining its benefits. It describes a novel organization of the scanner data into super-voxels (SV) that, combined with a super-voxel buffer (SVB), dramatically increase locality and prefetching, enable parallelism across SVs and lead to an average speedup of 187 on 20 cores.

Tomographic reconstruction, which involves computing a 3-D volume from its 2-D projections, is an important problem in imaging with wide-ranging applications, including medical scanners, electron microscopy, nondestructive testing, and transportation security. Model-based iterative reconstruction (MBIR) is a popular approach to 3-D reconstruction that has demonstrated the state-of-the-art reconstruction quality on several applications, and has been deployed in commercial healthcare systems. However, software implementations of MBIR on commodity general-purpose processors demonstrate poor performance due to its high compute and data requirements and cache unfriendly data access patterns. In this paper, we develop an efficient MBIR accelerator (EMBIRA) that achieves significant performance and energy improvement over software implementations. EMBIRA utilizes arrays of three types of specialized processing elements that match MBIR's computation patterns, and is further operated as a two-level nested pipeline to fully exploit the parallelism present in the algorithm. Another important source from which EMBIRA derives its efficiency is by constraining the sequence in which voxels1 in the 3-D volume are reconstructed. This enables better data reuse within the accelerator, thereby significantly reducing the number of off-chip memory accesses. To demonstrate the benefits of EMBIRA, we implemented a prototype on an Altera DE5 field-programmable gate array (FPGA) platform that includes an Altera Stratix V GX FPGA and DDR3 memory. Our implementation of EMBIRA, operating at 165 MHz, achieved 51.8× (5.8×) improvement in performance, and 355× (199×) improvement in energy, compared with optimized sequential (multithreaded) software implementations on a 48-core 2.3-GHz AMD Opteron-based server.

X-ray tomography is increasingly being used for 4D spatio-temporal imaging of material samples at micron and finer scales. However, the temporal resolution of widely used 4D reconstruction methods is severely limited by the need to acquire a very large number of views for each reconstructed 3D volume. In this paper, we present a time interlaced model-based iterative reconstruction (TIMBIR) method which can significantly improve the temporal resolution of reconstructions. TIMBIR is a synergistic combination of two innovations. The first innovation, interlaced view sampling, is a novel approach to data acquisition which distributes the view angles more evenly in time. The second innovation is a 4D model based iterative reconstruction algorithm (MBIR) which can produce time resolved volumetric reconstructions of the sample from the interlaced views. Reconstructions of simulated data indicate that TIMBIR can improve the temporal resolution by an order of magnitude relative to existing approaches.

Segmenting interesting objects from CT images has a wide range of applications. However, to achieve good results, it is often necessary to apply metal artifact reduction to raw CT images before segmentation. While there has been a great deal of research focusing on metal artifact reduction and segmentation as individual tasks, there have been very few attempts to solve the two problems jointly. We present a novel approach to solve the problem of segmenting raw CT images with metal artifacts, without the access to the raw CT data. Given an approximate metal artifact mask, the problem is formulated as a joint optimization over the restored image and the segmentation label, and the cost function includes a dictionary-based image prior to regularize the restored image and a continuous-relaxed Potts model for multi-class segmentation. An effective alternating method is used to solve the resulting optimization problem. The algorithm is applied to both simulated and real datasets and results show that it is effective in reducing metal artifacts and generating better segmentations simultaneously.

Many samples imaged in structural biology and material science contain several similar particles at random locations and orientations. Model-based iterative reconstruction (MBIR) methods can in principle be used to exploit such redundancies in images through log prior probabilities that accurately account for non-local similarity between the particles. However, determining such a log prior term can be challenging. Several denoising algorithms like non-local means (NLM) successfully capture such non-local redundancies, but the problem is two-fold: NLM is not explicitly formulated as a cost function, and neither can it capture similarity between randomly oriented particles. In this paper, we propose a rotationally-invariant nonlocal means (RINLM) algorithm, and describe a method to implement RINLM as a prior model using a novel framework that we call plug-and-play priors. We introduce the idea of patch pre-rotation to make RINLM computationally tractable. Finally, we showcase image denoising and 2D tomography results, using the proposed RINLM algorithm, as we highlight high reconstruction quality, image sharpness, and artifact suppression.

This paper introduces the vector sparse matrix transform (vector SMT), a new decorrelating transform suitable for performing distributed processing of high-dimensional signals in sensor networks. We assume that each sensor in the network encodes its measurements into vector outputs instead of scalar ones. The proposed transform decorrelates a sequence of pairs of vector outputs, until these vectors are decorrelated. In our experiments, we simulate distributed anomaly detection by a network of cameras, monitoring a spatial region. Each camera records an image of the monitored environment from its particular viewpoint and outputs a vector encoding the image. Our results, with both artificial and real data, show that the proposed vector SMT transform effectively decorrelates image measurements from the multiple cameras in the network while maintaining low overall communication energy consumption. Since it enables joint processing of the multiple vector outputs, our method provides significant improvements to anomaly detection accuracy when compared with the baseline case when the images are processed independently.

Here, we propose the vector Sparse Matrix Transform (SMT), a novel decorrelating transform suitable for performing distributed processing of high dimensional signals in sensor networks. We assume that each sensor in the network encodes its measurements into vector outputs instead of scalar ones. The proposed transform decorrelates a sequence of pairs of vector sensor outputs, until these vectors are decorrelated. In our experiments, we simulate distributed anomaly detection by a camera network monitoring a spatial region. Each camera records an image of the monitored environment from its particular viewpoint and outputs a vector encoding the image. Results show that the vector SMT effectively decorrelates images from the multiple cameras in the network and significantly improves anomaly detection accuracy while requiring low overall communication energy.

In many applications, it is critical to be able to sample the most informative pixels of an image first; and then once these pixels are sampled, the highest fidelity image can be reconstructed. Optimized sampling strategies generally fall into two categories: static and dynamic. In dynamic sampling, each new sample is chosen by using information obtained from previous samples. In this way, dynamic sampling offers the potential of much greater fidelity, but at the cost of greater complexity. Existing methods for dynamic non-uniform sampling of images are based on the intuition that sampling rates should be greatest in locations of greatest variation, but recent developments in the theory of optimal experimental design offer a theoretical framework for optimal sampling based on the use of a formal Bayesian prior model. In this paper, we introduce a fast dynamic image sampling framework based on Bayesian experimental design (BED). The method, which we call model-based dynamic sampling (MBDS) allows for the use of a general prior distribution for the image, and it incorporates a pixel-wise sampling constraint in the BED framework. The MBDS works by first generating L stochastic samples (i.e., images) from the posterior distribution given the current measurements, and then selecting the pixel with the greatest posterior variance. We also introduce a computationally efficient method for computing the stochastic samples through a local updating technique.

Synchrotron based X-ray tomography is widely used for three dimensional imaging of materials at the micron scale. Tomographic data collected from a synchrotron is often affected by non-idealities in the measurement system and sudden “blinding” of detector pixels during the acquisition. Typically, reconstructions are done using analytical reconstruction techniques combined with pre/post-processing steps to correct for the non-idealities, resulting in loss of detail while still producing noisy reconstructions with some artifacts. In this paper, we present a model-based iterative reconstruction (MBIR) algorithm for synchrotron X-ray tomography that can automatically handle the non-idealities as a part of the reconstruction. First, we develop a forward model that accounts for the non-idealities in the measurement system and for the occurrence of outliers in the measurement. Next, we combine the forward model with a prior model of the object to formulate the MBIR cost function and propose an algorithm to minimize the cost. Results on a real data set show that the MBIR reconstructions are superior to the analytical reconstructions effectively suppressing noise as well as other artifacts.

Tunable Diode Laser Absorption Spectroscopy (TDLAS) is an emerging technique for simultaneous sensing of temperature and concentration of gaseous media. However, simultaneous reconstruction of temperature and concentration using TDLAS measurements is a nonlinear inverse problem and unlike other forms of computed tomography (CT), it is typically not possible to take a large number of projection measurements; so reconstructions are often computed using simplistic assumptions that limit the usability of the results. In this paper, we present a fast algorithm for model-based iterative reconstruction (MBIR) of TDLAS data. Our TDLAS-MBIR method uses a nonlinear forward model based on the physics of light absorption and incorporates a holistic prior model that can be learned from very sparse training data. Reconstructions performed on computational fluid dynamics (CFD) phantoms show that our proposed reconstruction algorithm is fast; works well when the number of pixels, p, far exceeds the number of measurements, M; is robust against noise; and produces good reconstructions using few training examples for the prior model.

Many imaging applications require the implementation of space-varying convolution for accurate restoration and reconstruction of images. Here, we use the term space-varying convolution to refer to linear operators whose impulse response has slow spatial variation. In addition, these space-varying convolution operators are often dense, so direct implementation of the convolution operator is typically computationally impractical. One such example is the problem of stray light reduction in digital cameras, which requires the implementation of a dense space-varying deconvolution operator. However, other inverse problems, such as iterative tomographic reconstruction, can also depend on the implementation of dense space-varying convolution. While space-invariant convolution can be efficiently implemented with the fast Fourier transform, this approach does not work for space-varying operators. So direct convolution is often the only option for implementing space-varying convolution. In this paper, we develop a general approach to the efficient implementation of space-varying convolution, and demonstrate its use in the application of stray light reduction. Our approach, which we call matrix source coding, is based on lossy source coding of the dense space-varying convolution matrix. Importantly, by coding the transformation matrix, we not only reduce the memory required to store it; we also dramatically reduce the computation required to implement matrix-vector products. Our algorithm is able to reduce computation by approximately factoring the dense space-varying convolution operator into a product of sparse transforms. Experimental results show that our method can dramatically reduce the computation required for stray light reduction while maintaining high accuracy.

We have previously implemented the direct reconstruction of dense kinetic model parameter images ("parametric images") from sinogram data, and compared it to conventional image domain kinetic parameter estimation methods . Although it has been shown that the direct reconstruction algorithm estimates the kinetic model parameters with lower root mean squared error than the conventional image domain techniques, some theoretical obstacles remain. These obstacles include the difficulty of evaluating the accuracy and precision of the estimated parameters. In image domain techniques, the reconstructed time activity curve (TAC) and the model predicted TAC are compared, and the goodness-of-fit is evaluated as a measure of the accuracy and precision of the estimated parameters. This approach cannot be applied to the direct reconstruction technique as there are no reconstructed TACs. In this paper, we propose ways of evaluating the precision and goodness-of-fit of the kinetic model parameters estimated by the direct reconstruction algorithm. Specifically, precision of the estimates requires the calculation of variance images for each parameter, and goodness-of-fit is addressed by reconstructing the difference between the measured and the fitted sinograms. We demonstrate that backprojecting the difference from sinogram space to image space creates error images that can be examined for goodness-of-fit and model selection purposes. The presence of nonrandom structures in the error images may indicate an inadequacy of the kinetic model that has been incorporated into the direct reconstruction algorithm. We introduce three types of goodness-of-fit images. We propose and demonstrate a number-of-runs image as a means of quantifying the adequacy or deficiency of the model. We further propose and demonstrate images of the F statistic and the change in the Akaike Information Criterion as devices for identifying the statistical advantage of one model over another at each voxel. As direct reconstruction to parametric images proliferates, it will be essential for imagers to adopt methods such as those proposed herein to assess the accuracy and precision of their parametric images.

Dual-energy X-ray CT (DECT) has the potential to improve contrast and reduce artifacts as compared to traditional CT. Moreover, by applying model-based iterative reconstruction (MBIR) to dual-energy data, one might also expect to reduce noise and improve resolution. However, the direct implementation of dual-energy MBIR requires the use of a nonlinear forward model, which increases both complexity and computation. Alternatively, simplified forward models have been used which treat the material-decomposed channels separately, but these approaches do not fully account for the statistical dependencies in the channels. In this paper, we present a method for joint dual-energy MBIR (JDE-MBIR), which simplifies the forward model while still accounting for the complete statistical dependency in the material-decomposed sinogram components. The JDE-MBIR approach works by using a quadratic approximation to the polychromatic log-likelihood and a simple but exact nonnegativity constraint in the image domain. We demonstrate that our method is particularly effective when the DECT system uses fast kVp switching, since in this case the model accounts for the inaccuracy of interpolated sinogram entries. Both phantom and clinical results show that the proposed model produces images that compare favorably in quality to previous decomposition-based methods, including FBP and other statistical iterative approaches.

The JBIG2 standard is widely used for binary document image compression primarily because it achieves much higher compression ratios than conventional facsimile encoding standards. In this paper, we propose a dynamic hierarchical dictionary design method (DH) for multi-page binary document image compression with JBIG2. Our DH method outperforms other methods for multi-page compression by utilizing the information redundancy among pages with the following technologies. First, we build a hierarchical dictionary to keep more information per page for future usage. Second, we dynamically update the dictionary in memory to keep as much information as possible subject to the memory constraint. Third, we incorporate our conditional entropy estimation algorithm to utilize the saved information more effectively. Our experimental results show that the compression ratio improvement by our DH method is about 15% compared to the best existing multi-page encoding method.

Binarization algorithms are used to create a binary representation of a raster document image, typically with the intent of identifying text and separating it from background content. In this paper, we propose a binarization algorithm via one-pass local classification. The algorithm first generates the initial binarization results by local thresholding, then corrects the results by a one-pass local classification strategy, followed by the process of component inversion. The experimental results demonstrate that our algorithm achieves a somewhat lower binarization error rate than the state-of-the-art algorithm COS [1], while requiring significantly less computation.

High angle annular dark field (HAADF)-scanning transmission electron microscope (STEM) data is increasingly being used in the physical sciences to research materials in 3D because it reduces the effects of Bragg diffraction seen in bright field TEM data. Typically, tomographic reconstructions are performed by directly applying either filtered back projection (FBP) or the simultaneous iterative reconstruction technique (SIRT) to the data. Since HAADF-STEM tomography is a limited angle tomography modality with low signal to noise ratio, these methods can result in significant artifacts in the reconstructed volume. In this paper, we develop a model based iterative reconstruction algorithm for HAADF-STEM tomography. We combine a model for image formation in HAADF-STEM tomography along with a prior model to formulate the tomographic reconstruction as a maximum a posteriori probability (MAP) estimation problem. Our formulation also accounts for certain missing measurements by treating them as nuisance parameters in the MAP estimation framework. We adapt the iterative coordinate descent algorithm to develop an efficient method to minimize the corresponding MAP cost function. Reconstructions of simulated as well as experimental data sets show results that are superior to FBP and SIRT reconstructions, significantly suppressing artifacts and enhancing contrast.

We introduce the hypothesis selection filter (HSF) as a new approach for image quality enhancement. We assume that a set of filters has been selected a priori to improve the quality of a distorted image containing regions with different characteristics. At each pixel, HSF uses a locally computed feature vector to predict the relative performance of the filters in estimating the corresponding pixel intensity in the original undistorted image. The prediction result then determines the proportion of each filter used to obtain the final processed output. In this way, the HSF serves as a framework for combining the outputs of a number of different user selected filters, each best suited for a different region of an image. We formulate our scheme in a probabilistic framework where the HSF output is obtained as the Bayesian minimum mean square error estimate of the original image. Maximum likelihood estimates of the model parameters are determined from an offline fully unsupervised training procedure that is derived from the expectation-maximization algorithm. To illustrate how to apply the HSF and to demonstrate its potential, we apply our scheme as a post-processing step to improve the decoding quality of JPEG-encoded document images. The scheme consistently improves the quality of the decoded image over a variety of image content with different characteristics. We show that our scheme results in quantitative improvements over several other state-of-the-art JPEG decoding methods.

While Markov random field (MRF) models have been widely used in the solution of inverse problems, a major disadvantage of these models is the difficulty of parameter estimation. At its root, this parameter estimation problem stems from the inability to explicitly express the joint distribution of an MRF in terms of the conditional distributions of elements given their neighbors. The objective of this paper is to provide a general approach to solving maximum a posteriori (MAP) inverse problems through the implicit specification of a MRF prior. In this method, the MRF prior is implemented through a series of quadratic surrogate function approximations to the MRF's log prior distribution. The advantage of this approach is that these surrogate functions can be explicitly computed from the conditional probabilities of the MRF, while the explicit Gibbs distribution can not. Therefore, the Gibbs distribution remains only implicitly defined. In practice, this approach allows for more accurate modeling of data through the direct estimation of the MRF's conditional probabilities. We illustrate the application of our method with a simple experiments of image denoising and show that it produces superior results to some widely used MRF prior models.

Covariance estimation for high dimensional signals is a classically difficult problem in statistical signal analysis and machine learning. In this paper, we propose a maximum likelihood (ML) approach to covariance estimation, which employs a novel non-linear sparsity constraint. More specifically, the covariance is constrained to have an eigen decomposition which can be represented as a sparse matrix transform (SMT). The SMT is formed by a product of pairwise coordinate rotations known as Givens rotations. Using this framework, the covariance can be efficiently estimated using greedy optimization of the log-likelihood function, and the number of Givens rotations can be efficiently computed using a cross-validation procedure. The resulting estimator is generally positive definite and well-conditioned, even when the sample size is limited. Experiments on a combination of simulated data, standard hyperspectral data, and face image sets show that the SMT-based covariance estimates are consistently more accurate than both traditional shrinkage estimates and recently proposed graphical lasso estimates for a variety of different classes and sample sizes. An important property of the new covariance estimate is that it naturally yields a fast implementation of the estimated eigen-transformation using the SMT representation. In fact, the SMT can be viewed as a generalization of the classical fast Fourier transform (FFT) in that it uses "butterflies" to represent an orthonormal transform. However, unlike the FFT, the SMT can be used for fast eigen-signal analysis of general non-stationary signals.

The mixed raster content (MRC) standard (ITU-T T.44) specifies a framework for document compression which can dramatically improve the compression/quality tradeoff as compared to traditional lossy image compression algorithms. The key to MRC compression is the separation of the document into foreground and background layers, represented as a binary mask. Therefore, the resulting quality and compression ratio of a MRC document encoder is highly dependent upon the segmentation algorithm used to compute the binary mask. In this paper, we propose a novel multiscale segmentation scheme for MRC document encoding based upon the sequential application of two algorithms. The first algorithm, cost optimized segmentation (COS), is a blockwise segmentation algorithm formulated in a global cost optimization framework. The second algorithm, connected component classification (CCC), refines the initial segmentation by classifying feature vectors of connected components using an Markov random field (MRF) model. The combined COS/CCC segmentation algorithms are then incorporated into a multiscale framework in order to improve the segmentation accuracy of text with varying size. In comparisons to state-of-the-art commercial MRC products and selected segmentation algorithms in the literature, we show that the new algorithm achieves greater accuracy of text detection but with a lower false detection rate of nontext features. We also demonstrate that the proposed segmentation algorithm can improve the quality of decoded documents while simultaneously lowering the bit rate.

Recent applications of model-based iterative reconstruction (MBIR) algorithms to multislice helical CT reconstructions have shown that MBIR can greatly improve image quality by increasing resolution as well as reducing noise and some artifacts. However, high computational cost and long reconstruction times remain as a barrier to the use of MBIR in practical applications. Among the various iterative methods that have been studied for MBIR, iterative coordinate descent (ICD) has been found to have relatively low overall computational requirements due to its fast convergence. This paper presents a fast model-based iterative reconstruction algorithm using spatially nonhomogeneous ICD (NH-ICD) optimization. The NH-ICD algorithm speeds up convergence by focusing computation where it is most needed. The NH-ICD algorithm has a mechanism that adaptively selects voxels for update. First, a voxel selection criterion VSC determines the voxels in greatest need of update. Then a voxel selection algorithm VSA selects the order of successive voxel updates based upon the need for repeated updates of some locations, while retaining characteristics for global convergence. In order to speed up each voxel update, we also propose a fast 1-D optimization algorithm that uses a quadratic substitute function to upper bound the local 1-D objective function, so that a closed form solution can be obtained rather than using a computationally expensive line search algorithm. We examine the performance of the proposed algorithm using several clinical data sets of various anatomy. The experimental results show that the proposed method accelerates the reconstructions by roughly a factor of three on average for typical 3-D multislice geometries.

Recently, the Sparse Matrix Transform (SMT) has been proposed as a tool for estimating the eigen-decomposition of high dimensional data vectors. The SMT approach has two major advantages: First it can improve the accuracy of the eigendecomposition, particularly when the number of observations, n, is less the the vector dimension, p. Second, the resulting SMT eigen-decomposition is very fast to apply, i.e. O(p). In this paper, we present an SMT eigen-decomposition method suited for application to signals that live on graphs. This new SMT eigen-decomposition method has two major advantages over the more generic method presented in. First, the resulting SMT can be more accurately estimated due to the graphical constraint. Second, the computation required to design the SMT from training data is dramatically reduced from an average observed complexity of p3to p log p.

Regression from high dimensional observation vectors is particularly difficult when training data is limited. More specifically, if the number of sample vectors n is less than dimension of the sample vectors p, then accurate regression is difficult to perform without prior knowledge of the data covariance. In this paper, we propose a novel approach to high dimensional regression for application when n ≪ p. The approach works by first decorrelating the high dimensional observation vector using the sparse matrix transform (SMT) estimate of the data covariance. Then the decorrelated observations are used in a regularized regression procedure such as Lasso or shrinkage. Numerical results demonstrate that the proposed regression approach can significantly improve the prediction accuracy, especially when n is small and the signal to be predicted lies in the subspace of the observations corresponding to the small eigenvalues.

The Mixed Raster Content (MRC) standard (ITU-T T.44) specifies a framework for document compression which can dramatically improve the compression/quality tradeoff as compared to traditional lossy image compression algorithms. The key to MRC's performance is the separation of the document into foreground and background layers, represented as a binary mask. In this paper, we propose a novel multiscale segmentation scheme based on the sequential application of two algorithms. The first algorithm, Cost Optimized Segmentation (COS), is a blockwise segmentation algorithm formulated in a global cost optimization framework. The second algorithm, Connected Component Classification (CCC), refines the initial segmentation by classifying feature vectors of connected components using a Markov random field (MRF) model. The combined COS/CCC segmentation algorithms are then incorporated into a multiscale framework in order to improve the segmentation accuracy of text with varying size.

In this paper, we develop a classification method for high-dimensional data based on the Sparse Matrix Transform (SMT). The recently proposed SMT has been shown to produce more accurate estimates of covariance matrices when the number of training samples n is much less than the number of dimensions p of the data. Here we introduce a classifier that uses the SMT to model the covariance structure of the data. Experiments in face recognition using the FERET face database show that our method is superior to a conceptually very similar and low-dimensional method in at least two key aspects: First, the SMT classifier is more robust to the size of the training set, remaining accurate even when only a few training samples are available; Second, the total computation required to apply the SMT classifier to high-dimensional data is very low, making this method attractive for use in low-power and mobile devices, or in application settings requiring fast computation.

We investigate three algorithms that use the sparse matrix transform (SMT) to produce variance-maximizing linear projections to a lower-dimensional space. The SMT expresses the projection as a sequence of Givens rotations and this enables computationally efficient implementation of the projection operator. The baseline algorithm uses the SMT to directly approximate the optimal solution that is given by principal components analysis (PCA). A variant of the baseline begins with a standard SMT solution, but prunes the sequence of Givens rotations to only include those that contribute to the variance maximization. Finally, a simpler and faster third algorithm is introduced; this also estimates the projection operator with a sequence of Givens rotations, but in this case, the rotations are chosen to optimize a criterion that more directly expresses the dimension reduction criterion.

Conventional electrophotographic printers tend to produce Moiré artifacts when used for printing images scanned from printed material such as books and magazines. We propose a novel noniterative, nonlinear, and space-variant descreening filter that removes a wide range of Moiré-causing screen frequencies in a scanned document while preserving image sharpness and edge detail. This filter is inspired by Perona-Malik's anisotropic diffusion equation. The amount of diffusion of the image intensity resulting from applying the filter is governed by an edge intensity estimate that is robust under halftone noise. More precisely, the filter extracts a spatial feature vector comprising local intensity gradients estimated from a local window in a presmoothed version of the noisy input image. Tunable nonlinear polynomial functions of this feature vector are then used to perform one iteration of a discrete diffusion controlled by the intensity gradient. The polynomial functions and feature extraction kernels are selected empirically in order to minimize computation while ensuring robust performance across a wide range of test images on a target imaging platform. The algorithm uses integer arithmetic, mostly relying on low-cost bit-wise shift and addition operations, and uses a strictly sequential architecture to provide a cost-effective and robust descreening solution in practical imaging devices including copiers and multifunction printers. We compare the performance of the proposed algorithm to other descreening solutions and demonstrate that the new algorithm improves quality over the existing methods while reducing computation.

We present a method for noniterative maximum a posteriori (MAP) tomographic reconstruction which is based on the use of sparse matrix representations. Our approach is to precompute and store the inverse matrix required for MAP reconstruction. This approach has generally not been used in the past because the inverse matrix is typically large and fully populated (i.e., not sparse). In order to overcome this problem, we introduce two new ideas. The first idea is a novel theory for the lossy source coding of matrix transformations which we refer to as matrix source coding. This theory is based on a distortion metric that reflects the distortions produced in the final matrix-vector product, rather than the distortions in the coded matrix itself. The resulting algorithms are shown to require orthonormal transformations of both the measurement data and the matrix rows and columns before quantization and coding. The second idea is a method for efficiently storing and computing the required orthonormal transformations, which we call a sparse-matrix transform (SMT). The SMT is a generalization of the classical FFT in that it uses butterflies to compute an orthonormal transform; but unlike an FFT, the SMT uses the butterflies in an irregular pattern, and is numerically designed to best approximate the desired transforms. We demonstrate the potential of the noniterative MAP reconstruction with examples from optical tomography. The method requires offline computation to encode the inverse transform. However, once these offline computations are completed, the noniterative MAP algorithm is shown to reduce both storage and computation by well over two orders of magnitude, as compared to a linear iterative reconstruction methods.

The JPEG standard is one of the most prevalent image compression schemes in use today. While JPEG was designed for use with natural images, it is also widely used for the encoding of raster documents. Unfortunately, JPEG's characteristic blocking and ringing artifacts can severely degrade the quality of text and graphics in complex documents. We propose a JPEG decompression algorithm which is designed to produce substantially higher quality images from the same standard JPEG encodings. The method works by incorporating a document image model into the decoding process which accounts for the wide variety of content in modern complex color documents. The method works by first segmenting the JPEG encoded document into regions corresponding to background, text, and picture content. The regions corresponding to text and background are then decoded using maximum a posteriori (MAP) estimation. Most importantly, the MAP reconstruction of the text regions uses a model which accounts for the spatial characteristics of text and graphics. Our experimental comparisons to the baseline JPEG decoding as well as to three other decoding schemes, demonstrate that our method substantially improves the quality of decoded images, both visually and as measured by PSNR.

Conventional electrophotographic printers tend to produce Moire artifacts when used for printing images scanned from printed material such as books and magazines. Inspired by anisotropic diffusion, we propose a novel non-iterative, non-linear, and space-variant de- screening filter that removes a wide range of Moire-causing screen frequencies in a scanned document while preserving image sharpness and edge detail. The amount of diffusion of the image intensity resulting from applying the filter is governed by an estimate of the gradient that is robust under halftone noise. More precisely, the filter extracts a spatial feature vector comprising local intensity gradients estimated from a local window in a pre-smoothed version of the noisy input image. Tunable non-linear polynomial functions of this feature vector are then used to perform one iteration of a discrete diffusion controlled by the intensity gradient. We compare the performance of the proposed algorithm to other descreening solutions and demonstrate that the new algorithm improves quality over the existing methods while reducing computation.

Covariance estimation for high dimensional vectors is a classically difficult problem in statistical analysis and machine learning due to limited sample size. In this paper, we propose a new approach to covariance estimation, which is based on constrained maximum likelihood (ML) estimation of the covariance. Specifically, the covariance is constrained to have an eigen decomposition which can be represented as a sparse matrix transform (SMT). The SMT is formed by a product of pairwise coordinate rotations known as Givens rotations. Using this framework, the covariance can be efficiently estimated using greedy minimization of the log likelihood function, and the number of Givens rotations can be efficiently computed using a cross-validation procedure. The estimator obtained using this method is always positive definite and well-conditioned even with limited sample size. Experiments on hyperspectral data show that SMT covariance estimation results in consistently better estimates of the covariance for a variety of different classes and sample sizes compared to traditional shrinkage estimators.

Imaging research, development, and applications are growing at an astounding rate, and image-processing researchers can take credit for having created much of the enabling technologies that have fueled this growth. The development of image and video coding standards, such as JPEG and MPEG, has enabled the web as a center for commerce and entertainment. Ubiquitous technologies, such as Direct TV, DVDs, BlueRay, and TiVo, depend on these standards; streaming Internet video services, like Tunes' recently announced movie rental feature, are well on their way to replacing traditional analog broadcast video. Other consumer products, such as home printers, digital cameras, and mobile video devices, have each been a major disruptive product enabled by fundamental innovation from image-processing researchers.

In this paper, we propose a hierarchical color correction algorithm for enhancing the color of digital images obtained from low-quality digital image capture devices such as cell phone cameras. The proposed method is based on a multilayer hierarchical stochastic framework whose parameters are learned in an offline training procedure using the well-known expectation maximization (EM) algorithm. This hierarchical framework functions by first making soft assignments of images into defect classes and then processing the images in each defect class with an optimized algorithm. The hierarchical color correction is performed in three stages. In the first stage, global color attributes of the low-quality input image are used in a Gaussian mixture model (GMM) framework to perform a soft classification of the image into M predefined global image classes. In the second stage, the input image is processed with a nonlinear color correction algorithm that is designed for each of the M global classes. This color correction algorithm, which we refer to as resolution synthesis color correction (RSCC), applies a spatially varying color correction determined by the local color attributes of the input image. In the third stage, the outputs of the RSCC predictors are combined using the global classification weights to yield the color corrected output image. We compare the performance of the proposed method to other commercial color correction algorithms on cell phone camera images obtained from different sources. Both subjective and objective measures of quality indicate that the new color correction algorithm improves quality over the existing methods.

In this paper, we propose a method for improving the color rendition of low quality cell phone camera images. The proposed method is based on a multi layer stochastic framework whose parameters are learned in an offline training procedure using the well known expectation maximization (EM) algorithm. The color correction algorithm functions by first making soft assignments of images into defect classes and then processing images in each defect class with an optimized algorithm, which we refer to as resolution synthesis-based color correction (RSCC). The parameters of the color correction algorithm are trained using pairs of low quality images, obtained from real cell phone cameras, and high quality spatially registered reference images, captured with a high quality digital still camera. We present experimental results comparing the performance of our method to some existing commercial color correction algorithms.

This paper describes a real-time, strip-based, low-complexity document page classification algorithm, which can be used as a copy mode selector in the copy pipeline. The benefits of such a copy mode selector include improving copy quality, simplifying user interaction, and increasing copy rate.

We present a novel probabilistic model for the hierarchal structure of an image and its regions. We call this model spatial random tree grammars (SRTGs). We develop algorithms for exact computation of likelihoods and MAP estimates and exact EM updates for model-parameter estimation. We collectively call these algorithms the center-surround algorithm. We use the center-surround algorithm to automatically estimate the ML parameters of SRTGs, classify images based on their likelihood and based on the MAP estimate of the associated hierarchal structure. We apply our method to the task of classifying natural images and demonstrate that the addition of hierarchal structure significantly improves upon the performance of a baseline model that lacks such structure.

Conventional halftoning methods employed in electrophotographic printers tend to produce Moiré artifacts when used for printing images scanned from printed material, such as books and magazines. We present a novel approach for descreening color scanned documents aimed at providing an efficient solution to the Moiré problem in practical imaging devices, including copiers and multifunction printers. The algorithm works by combining two nonlinear image-processing techniques, resolution synthesis-based denoising (RSD), and modified smallest univalue segment assimilating nucleus (SUSAN) filtering. The RSD predictor is based on a stochastic image model whose parameters are optimized beforehand in a separate training procedure. Using the optimized parameters, RSD classifies the local window around the current pixel in the scanned image and applies filters optimized for the selected classes. The output of the RSD predictor is treated as a first-order estimate to the descreened image. The modified SUSAN filter uses the output of RSD for performing an edge-preserving smoothing on the raw scanned data and produces the final output of the descreening algorithm. Our method does not require any knowledge of the screening method, such as the screen frequency or dither matrix coefficients, that produced the printed original. The proposed scheme not only suppresses the Moiré artifacts, but, in addition, can be trained with intrinsic sharpening for deblurring scanned documents. Finally, once optimized for a periodic clustered-dot halftoning method, the same algorithm can be used to inverse halftone scanned images containing stochastic error diffusion halftone noise.

We have developed a nonparametric approach to the analysis of dynamic positron emission tomography (PET) data for extracting temporal characteristics of the change in endogenous neurotransmitter concentration in the brain. An algebraic method based on singular value decomposition (SVD) was applied to simulated data under both rest (neurotransmitter at baseline) and activated (transient neurotransmitter release) conditions. The resulting signals are related to the integral of the change in free neurotransmitter concentration in the tissue. Therefore, a specially designed minimum mean-square error (MMSE) filter must be applied to the signals to recover the desired temporal pattern of neurotransmitter change. To test the method, we simulated sets of realistic time activity curves representing uptake of [11C]raclopride, a dopamine (DA) receptor antagonist, in brain regions, under baseline and dopamine-release conditions. Our tests considered two scenarios: 1) a spatially homogeneous pattern with all voxels in the activated state presenting an identical DA signal; 2) a spatially heterogeneous pattern in which different DA signals were contained in different families of voxels. In the first case, we demonstrated that the timing of a single DA peak can be accurately identified to within 1 min and that two distinct neurotransmitter peaks can be distinguished. In the second case, separate peaks of activation separated by as little as 5 min can be distinguished. A decrease in blood flow during activation could not account for our findings. We applied the method to human PET data acquired with [11C]raclopride in the presence of transiently elevated DA due to intravenous (IV) alcohol. Our results for an area of the nucleus accumbens-a region relevant to alcohol consumption-agreed with a model-based method for estimating the DA response. SVD-based analysis of dynamic PET data promises a completely noninvasive and model-independent technique for determining the dynamics of a neurotransmitter response to cognitive or pharmacological stimuli. Our results indicate that the method is robust enough for application to voxel-by-voxel data.

The mixed raster content (MRC) model can be used to implement highly effective document compression algorithms. MRC document coders are typically based on the use of a binary mask layer that efficiently encodes the text and graphic content. However, while many MRC-based methods can yield much higher compression ratios than conventional color image compression methods, the binary representation tends to distort fine document details, such as thin lines and text edges. In this paper, we propose a method for encoding and decoding the binary mask layer that substantially improves the decoded document fidelity of text and graphics at a fixed bit rate. This method, which we call resolution-enhanced rendering (RER), works by adaptively dithering the encoded binary mask, and then applying a nonlinear predictor to decode a gray level mask at the same resolution. Both the dithering and nonlinear prediction algorithms are jointly optimized to produce the minimal distortion rendering. In addition, we introduce a second method, interpolative RER (IRER), which incorporates interpolation into the MRC decoder. The IRER method increases the compression ratio by allowing a high-resolution document to be coded at lower resolutions. We present experimental results illustrating the performance of our RER/IRER methods and comparing them to some existing MRC-based compression algorithms.

We address the best basis problem--or, more generally, the best representation problem: Given a signal, a dictionary of representations, and an additive cost function, the aim is to select the representation from the dictionary which minimizes the cost for the given signal. We develop a new framework of multitree dictionaries, which includes some previously proposed dictionaries as special cases. We show how to efficiently find the best representation in a multitree dictionary using a recursive tree-pruning algorithm. We illustrate our framework through several examples, including a novel block image coder, which significantly outperforms both the standard JPEG and quadtree-based methods and is comparable to embedded coders such as JPEG2000 and SPIHT.

A multigrid inversion approach that uses variable resolutions of both the data space and the image space is proposed. Since the computational complexity of inverse problems typically increases with a larger number of unknown image pixels and a larger number of measurements, the proposed algorithm further reduces the computation relative to conventional multigrid approaches, which change only the image space resolution at coarse scales. The advantage is particularly important for data-rich applications, where data resolutions may differ for different scales. Applications of the approach to Bayesian reconstruction algorithms in transmission and emission tomography with a generalized Gaussian Markov random field image prior are presented, both with a Poisson noise model and with a quadratic data term. Simulation results indicate that the proposed multigrid approach results in significant improvement in convergence speed compared to the fixed-grid iterative coordinate descent method and a multigrid method with fixed-data resolution.

We develop a new class of hierarchical stochastic image models called spatial random trees (SRTs) which admit polynomial-complexity exact inference algorithms. Our framework of multitree dictionaries is the starting point for this construction. SRTs are stochastic hidden tree models whose leaves are associated with image data. The states at the tree nodes are random variables, and, in addition, the structure of the tree is random and is generated by a probabilistic grammar. We describe an efficient recursive algorithm for obtaining the maximum a posteriori estimate of both the tree structure and the tree states given an image. We also develop an efficient procedure for performing one iteration of the expectation-maximization algorithm and use it to estimate the model parameters from a set of training images. We address other inference problems arising in applications such as maximization of posterior marginals and hypothesis testing. Our models and algorithms are illustrated through several image classification and segmentation experiments, ranging from the segmentation of synthetic images to the classification of natural photographs and the segmentation of scanned documents. In each case, we show that our method substantially improves accuracy over a variety of existing methods.

We use the framework of multitree dictionaries (Huang et al. (2003)) to design a novel DCT-based image coder which significantly outperforms both the standard JPEG and the quadtree-based approach of Ramchandran et al. (1993).

In vivo optical molecular imaging involves the use of light emitting tracers combined with sophisticated sensing modalities to perform in vivo imaging of genetic and molecular information. In contrast to the classical diagnostic imaging tools which image the end effects of the diseases, optical molecular imaging could enhance our knowledge of biological phenomena, monitor genetic expression and the alteration of cells, and lead to earlier detection of diseases. With the development of exotic molecular probes with easily detectable bioluminescence and fluorescence labels, optical molecular imaging has emerged as an important new field within biomedical imaging. This paper reviews this state-of-the-art imaging technology and signal processing issues to monitor molecular and cellular events in living organisms.

We generalize our results of [Y. Huang et al, 2005 and 2003] and propose a new framework of multitree dictionaries which include many previously proposed dictionaries as well as many new, very large, tree-structured dictionaries. We present an efficient, globally optimal algorithm to find the best tree in such a dictionary. We describe a novel block image coder based on our framework, which is an improvement over our image coder presented in Y. Huang et al, (2005).

A variety of new imaging modalities, such as optical diffusion tomography, require the inversion of a forward problem that is modeled by the solution to a three-dimensional partial differential equation. For these applications, image reconstruction is particularly difficult because the forward problem is both nonlinear and computationally expensive to evaluate. In this paper, we propose a general framework for nonlinear multigrid inversion that is applicable to a wide variety of inverse problems. The multigrid inversion algorithm results from the application of recursive multigrid techniques to the solution of optimization problems arising from inverse problems. The method works by dynamically adjusting the cost functionals at different scales so that they are consistent with, and ultimately reduce, the finest scale cost functional. In this way, the multigrid inversion algorithm efficiently computes the solution to the desired fine-scale inversion problem. Importantly, the new algorithm can greatly reduce computation because both the forward and inverse problems are more coarsely discretized at lower resolutions. An application of our method to Bayesian optical diffusion tomography with a generalized Gaussian Markov random-field image prior model shows the potential for very large computational savings. Numerical data also indicates robust convergence with a range of initialization conditions for this nonconvex optimization problem.

Our goal in this paper is the estimation of kinetic model parameters for each voxel corresponding to a dense three-dimensional (3-D) positron emission tomography (PET) image. Typically, the activity images are first reconstructed from PET sinogram frames at each measurement time, and then the kinetic parameters are estimated by fitting a model to the reconstructed time-activity response of each voxel. However, this "indirect" approach to kinetic parameter estimation tends to reduce signal-to-noise ratio (SNR) because of the requirement that the sinogram data be divided into individual time frames. In 1985, Carson and Lange proposed, but did not implement, a method based on the expectation-maximization (EM) algorithm for direct parametric reconstruction. The approach is "direct" because it estimates the optimal kinetic parameters directly from the sinogram data, without an intermediate reconstruction step. However, direct voxel-wise parametric reconstruction remained a challenge due to the unsolved complexities of inversion and spatial regularization. In this paper, we demonstrate and evaluate a new and efficient method for direct voxel-wise reconstruction of kinetic parameter images using all frames of the PET data. The direct parametric image reconstruction is formulated in a Bayesian framework, and uses the parametric iterative coordinate descent (PICD) algorithm to solve the resulting optimization problem. The PICD algorithm is computationally efficient and is implemented with spatial regularization in the domain of the physiologically relevant parameters. Our experimental simulations of a rat head imaged in a working small animal scanner indicate that direct parametric reconstruction can substantially reduce root-mean-squared error (RMSE) in the estimation of kinetic parameters, as compared to indirect methods, without appreciably increasing computation.

We propose a best basis search algorithm for local cosine dictionaries. We improve upon the classical best local cosine basis selection based on a dyadic tree (Coifman, R.R. and Wickerhauser, M.V., IEEE Trans. Inf. Th., vol.38, no.2, p.713-18, 1992), by considering a larger dictionary of bases. This results in more compact representations, lower costs, and approximate shift-invariance. We also provide a version of our algorithm which is strictly shift-invariant.

A common method of increasing hemodynamic response (SNR) in functional magnetic resonance imaging (fMRI) is to average signal timecourses across voxels. This technique is potentially problematic because the hemodynamic response may vary across the brain. Such averaging may destroy significant features in the temporal evolution of the fMRI response that stem from either differences in vascular coupling to neural tissue or actual differences in the neural response between two averaged voxels. Two novel techniques are presented in this paper in order to aid in an improved SNR estimate of the hemodynamic response while preserving statistically significant voxel-wise differences. The first technique is signal subspace estimation for periodic stimulus paradigms that involves a simple thresholding method. This increases SNR via dimensionality reduction. The second technique that we call clustered components analysis is a novel amplitude-independent clustering method based upon an explicit statistical data model. It includes an unsupervised method for estimating the number of clusters. Our methods are applied to simulated data for verification and comparison to other techniques. A human experiment was also designed to stimulate different functional cortices. Our methods separated hemodynamic response signals into clusters that tended to be classified according to tissue characteristics.

In this paper, we describe a unique new paradigm for video database management known as ViBE (video indexing and browsing environment). ViBE is a browseable/searchable paradigm for organizing video data containing a large number of sequences. The system first segments video sequences into shots by using a new feature vector known as the Generalized Trace obtained from the DC-sequence of the compressed data. Each video shot is then represented by a hierarchical structure known as the shot tree. The shots are then classified into pseudo-semantic classes that describe the shot content. Finally, the results are presented to the user in an active browsing environment using a similarity pyramid data structure. The similarity pyramid allows the user to view the video database at various levels of detail. The user can also define semantic classes and reorganize the browsing environment based on relevance feedback. We describe how ViBE performs on a database of MPEG sequences.

A new class of multiscale multidimensional stochastic processes called spatial random trees is introduced. The model is based on multiscale stochastic trees with stochastic structure as well as stochastic states. Procedures are developed for exact likelihood calculation, MAP estimation of the process, and estimation of the parameters of the process. The new framework is illustrated through a simple binary image classification problem.

In this paper, we propose a general framework for nonlinear multigrid inversion applicable to any inverse problem in which the forward model can be naturally represented at differing resolutions. In multigrid inversion, the problem is adjusted to be solved at each resolution by using the solutions at both finer and coarser resolutions. To do this, we formulate a consistent set of coarse scale cost functionals to ultimately reduce the finest scale one. At each resolution, both the forward model and inverse problems are discretized at the lower resolution; thus reducing computation. Our simulation results for the application of optical diffusion tomography indicate the potential for fast and robust convergence.

A new class of multiscale multidimensional stochastic processes called spatial random trees was recently introduced in J. Pollak et al. (2003). The model is based on multiscale stochastic trees with stochastic structure as well as stochastic states. In this work, we describe a method for estimating the parameters of the process.

We quantitatively compare filtered backprojection (FBP), expectation-maximization (EM), and Bayesian reconstruction algorithms as applied to the IndyPET scanner--a dedicated research scanner which has been developed for small and intermediate field of view imaging applications. In contrast to previous approaches that rely on Monte Carlo simulations, a key feature of our investigation is the use of an empirical system kernel determined from scans of line source phantoms. This kernel is incorporated into the forward model of the EM and Bayesian algorithms to achieve resolution recovery. Three data sets are used, data collected on the IndyPET scanner using a bar phantom and a Hoffman three-dimensional brain phantom, and simulated data containing a hot lesion added to a uniform background. Reconstruction quality is analyzed quantitatively in terms of bias-variance measures (bar phantom) and mean square error (lesion phantom). We observe that without use of the empirical system kernel, the FBP, EM, and Bayesian algorithms give similar performance. However, with the inclusion of the empirical kernel, the iterative algorithms provide superior reconstructions compared with FBP, both in terms of visual quality and quantitative measures. Furthermore, Bayesian methods outperform EM. We conclude that significant improvements in reconstruction quality can be realized by combining accurate models of the system response with Bayesian reconstruction algorithms.

We introduce an adaptive wavelet graph image model applicable to Bayesian tomographic reconstruction and other problems with nonlocal observations. The proposed model captures coarse-to-fine scale dependencies in the wavelet tree by modeling the conditional distribution of wavelet coefficients given overlapping windows of scaling coefficients containing coarse scale information. This results in a graph dependency structure which is more general than a quadtree, enabling the model to produce smooth estimates even for simple wavelet bases such as the Haar basis. The inter-scale dependencies of the wavelet graph model are specified using a spatially nonhomogeneous Gaussian distribution with parameters at each scale and location. The parameters of this distribution are selected adaptively using nonlinear classification of coarse scale data. The nonlinear adaptation mechanism is based on a set of training images. In conjunction with the wavelet graph model, we present a computationally efficient multiresolution image reconstruction algorithm. This algorithm is based on iterative Bayesian space domain optimization using scale recursive updates of the wavelet graph prior model. In contrast to performing the optimization over the wavelet coefficients, the space domain formulation facilitates enforcement of pixel positivity constraints. Results indicate that the proposed framework can improve reconstruction quality over fixed resolution Bayesian methods.

We introduce a new approach to optimal image scaling called resolution synthesis (RS). In RS, the pixel being interpolated is first classified in the context of a window of neighboring pixels; and then the corresponding high-resolution pixels are obtained by filtering with coefficients that depend upon the classification. RS is based on a stochastic model explicitly reflecting the fact that pixels falls into different classes such as edges of different orientation and smooth textures. We present a simple derivation to show that RS generates the minimum mean-squared error (MMSE) estimate of the high-resolution image, given the low-resolution image. The parameters that specify the stochastic model must be estimated beforehand in a training procedure that we have formulated as an instance of the well-known expectation-maximization (EM) algorithm. We demonstrate that the model parameters generated during the training may be used to obtain superior results even for input images that were not used during the training.

Raster document coders are typically based on the use of a binary mask layer that efficiently encodes the text and graphic content. While these methods can yield much higher compression ratios than natural image compression methods, the binary representation tends to distort fine document details, such as thin lines, and text edges. In this paper, we describe a method for encoding and decoding the binary mask layer that substantially improves the decoded document quality at a fixed bit rate. This method, which we call resolution enhanced rendering (RER), works by adaptively dithering the encoded binary mask, and then applying a nonlinear predictor to decode a gray level mask at the same or higher resolution. We present experimental results illustrating that the RER method can substantially improve document quality at high compression ratios.

Multiscale Bayesian approaches have attracted increasing attention for use in image segmentation. Generally, these methods tend to offer improved segmentation accuracy with reduced computational burden. Existing Bayesian segmentation methods use simple models of context designed to encourage large uniformly classified regions. Consequently, these context models have a limited ability to capture the complex contextual dependencies that are important in applications such as document segmentation. We propose a multiscale Bayesian segmentation algorithm which can effectively model complex aspects of both local and global contextual behavior. The model uses a Markov chain in scale to model the class labels that form the segmentation, but augments this Markov chain structure by incorporating tree based classifiers to model the transition probabilities between adjacent scales. The tree based classifier models complex transition rules with only a moderate number of parameters. One advantage to our segmentation algorithm is that it can be trained for specific segmentation applications by simply providing examples of images with their corresponding accurate segmentations. This makes the method flexible by allowing both the context and the image models to be adapted without modification of the basic algorithm. We illustrate the value of our approach with examples from document segmentation in which test, picture and background classes must be separated.

Optical diffusion tomography is a technique for imaging a highly scattering medium using measurements of transmitted modulated light. Reconstruction of the spatial distribution of the optical properties of the medium from such data is a difficult nonlinear inverse problem. Bayesian approaches are effective, but are computationally expensive, especially for three-dimensional (3-D) imaging. This paper presents a general nonlinear multigrid optimization technique suitable for reducing the computational burden in a range of nonquadratic optimization problems. This multigrid method is applied to compute the maximum a posteriori (MAP) estimate of the reconstructed image in the optical diffusion tomography problem. The proposed multigrid approach both dramatically reduces the required computation and improves the reconstructed image quality.

The objective of this work is to provide a simple and yet efficient tool to detect human faces in video sequences. This information can be very useful for many applications such as video indexing and video browsing. In particular the paper focuses on the significant improvements made to our face detection algorithm presented by Albiol, Bouman and Delp (see IEEE Int. Conference on Image Processing, Kobe, Japan, 1999). Specifically, a novel approach to retrieve skin-like homogeneous regions is presented, which is later used to retrieve face images. Good results have been obtained for a large variety of video sequences.

In this paper, we introduce a method for estimating the statistically distinct neural responses in an sequence of functional magnetic resonance images (fMRI). The crux of our method is a technique which we call clustered component analysis (CCA). Clustered component analysis is a method for identifying the distinct component vectors in a multivariate data set. CCA is distinct from principal components analysis (PCA), and independent components analysis (ICA), because it is not constrained to produce orthogonal component vectors and it does not assume that components are independent. CCA employs Bayesian estimation methods such as expectation-maximization (EM) and Rissanen order identification to determine the best set of component vectors.

We introduce a spatially non-homogeneous adaptive image model and multiresolution reconstruction algorithm for Bayesian tomographic reconstruction. In contrast to existing approaches, the proposed image model is formulated in a multiresolution wavelet domain and relies on training data to incorporate the expected characteristics of typical reconstructions. The actual tomographic reconstruction is performed in the space domain to simplify enforcement of the positivity constraint. We apply the proposed algorithm to simulated data and to data acquired using the IndyPET dedicated research scanner. Our experimental results indicate that our algorithm can improve reconstruction quality over fixed resolution Bayesian methods.

The advent of large image databases (>10000) has created a need for tools which can search and organize images automatically by their content. This paper focuses on the use of hierarchical tree-structures to both speed-up search-by-query and organize databases for effective browsing. The first part of this paper develops a fast search algorithm based on best-first branch and bound search. This algorithm is designed so that speed and accuracy may be continuously traded-off through the selection of a parameter lambda. We find that the algorithm is most effective when used to perform an approximate search, where it can typically reduce computation by a factor of 20-40 for accuracies ranging from 80% to 90%. We then present a method for designing a hierarchical browsing environment which we call a similarity pyramid. The similarity pyramid groups similar images together while allowing users to view the database at varying levels of resolution. We show that the similarity pyramid is best constructed using agglomerative (bottom up) clustering methods, and present a fast sparse clustering method which dramatically reduces both memory and computation over conventional methods.

Bayesian tomographic reconstruction algorithms generally require the efficient optimization of a functional of many variables. In this setting, as well as in many other optimization tasks, functional substitution (FS) has been widely applied to simplify each step of the iterative process. The function to be minimized is replaced locally by an approximation having a more easily manipulated form, e.g., quadratic, but which maintains sufficient similarity to descend the true functional while computing only the substitute. We provide two new applications of FS methods in iterative coordinate descent for Bayesian tomography. The first is a modification of our coordinate descent algorithm with one-dimensional (1-D) Newton-Raphson approximations to an alternative quadratic which allows convergence to be proven easily. In simulations, we find essentially no difference in convergence speed between the two techniques. We also present a new algorithm which exploits the FS method to allow parallel updates of arbitrary sets of pixels using computations similar to iterative coordinate descent. The theoretical potential speed up of parallel implementations is nearly linear with the number of processors if communication costs are neglected.

Pseudo-semantic labeling represents a novel approach for automatic content description of video. This information can be used in the context of a video database to improve browsing and searching. In this paper we describe our work on using face detection techniques for pseudo-semantic labeling. We present our results using a database of MPEG sequences.

In this research, rather than developing a forward model to be inverted, we propose directly modeling the inverse operator. The goal is to develop a non-iterative Bayesian reconstruction method which requires computation comparable to conventional FBP methods, but achieves quality competitive with that of iterative Bayesian methods such as maximum a posteriori probability (MAP). The method we propose, which we call nonlinear back projection (NBP), forms a back projected image cross-section by applying nonlinear filters to the projected data. This method attempts to directly model a type of optimal inverse operator through off-line training of the non-linear filters using example training data of known image cross sections and noisy realizations of projections. The Radon domain filtering is two-dimensional, exploiting redundancy among adjacent angles' measurements. This direct approach to modeling the inverse operator has several potential advantages which make it interesting. First, the elimination of iterative estimation should save computation time relative to common Bayesian techniques. Secondly, some of the inherently nonlinear attributes of the forward process may be implicitly incorporated into the training of the nonlinear backprojection. Finally, training based on sample images and projections may more effectively incorporate greater complexity in the statistical behavior of images than the simple Markov random field models found in most Bayesian formulations.

In this paper, we propose a multilayer document compression algorithm. This algorithm first segments a scanned document image into different classes such as text, images and background, then compresses each class using an algorithm specifically designed for that class. Two algorithms are investigated for segmenting documents: a general purpose image segmentation algorithm called the trainable sequential MAP (TSMAP) algorithm, and a rate-distortion optimized segmentation (RDOS) algorithm. Experimental results show that the multilayer compression algorithm can achieve a much lower bit rate than most conventional algorithms such as JPEG at similar subjective distortion levels. We also find that the RDOS method produces more robust segmentations than TSMBP by eliminating misclassifications which can sometimes cause severe artifacts.

Optical diffusion tomography attempts to reconstruct an object cross section (a highly scattering media such as tissue) from measurements of scattered and attenuated light. While Bayesian approaches are well suited to this difficult nonlinear inverse problem, the resulting optimization problem is very computationally expensive. In this paper, we propose a nonlinear multigrid technique for computing the maximum a posteriori (MAP) reconstruction in the optical diffusion tomography problem. The multigrid approach improves reconstruction quality by avoiding a local minimum. In addition, it dramatically reduces computation. Each iteration of the algorithm alternates a Born approximation step with a single cycle of a nonlinear multigrid algorithm.

Most previous approaches to Bayesian segmentation have used simple prior models, such as Markov random fields (MRF), to enforce regularity in the segmentation. While these methods improve classification accuracy, they are not well suited to modeling complex contextual structure. In this paper, we propose a context model for multiscale segmentation which can capture very complex behaviors on both local and global scales. Our method works by using binary classification trees to model the transition probabilities between segmentations at adjacent scales. The classification trees can be efficiently trained to model essential aspects of contextual behavior. In addition, the data model in our approach is novel in the sense that it can incorporate the correlation among the wavelet feature vectors across scales. We apply our method to the problem of document segmentation to illustrate its usefulness.

Markov random fields (MRF's) have been widely used to model images in Bayesian frameworks for image reconstruction and restoration. Typically, these MRF models have parameters that allow the prior model to be adjusted for best performance. However, optimal estimation of these parameters(sometimes referred to as hyper parameters) is difficult in practice for two reasons: i) direct parameter estimation for MRF's is known to be mathematically and numerically challenging; ii)parameters can not be directly estimated because the true image cross section is unavailable.In this paper, we propose a computationally efficient scheme to address both these difficulties for a general class of MRF models,and we derive specific methods of parameter estimation for the MRF model known as generalized Gaussian MRF (GGMRF).The first section of the paper derives methods of direct estimation of scale and shape parameters for a general continuously valued MRF. For the GGMRF case, we show that the ML estimate of the scale parameter, sigma, has a simple closed-form solution, and we present an efficient scheme for computing the ML estimate of the shape parameter, p, by an off-line numerical computation of the dependence of the partition function on p.The second section of the paper presents a fast algorithm for computing ML parameter estimates when the true image is unavailable. To do this, we use the expectation maximization(EM) algorithm. We develop a fast simulation method to replace the E-step, and a method to improve parameter estimates when the simulations are terminated prior to convergence.Experimental results indicate that our fast algorithms substantially reduce computation and result in good scale estimates for real tomographic data sets.

Many halftoning algorithms tend to render highlight regions with objectionable dot distributions. To alleviate this artifact, we introduce a halftone postprocessing algorithm called the Springs algorithm. The objective of Springs is to rearrange dots in affected regions for a smoother more attractive rendition. We describe the Springs algorithm, and we show results which demonstrate its effectiveness. The heart of this algorithm is a simple dot-rearrangement heuristic which results in a more isotropic dot distribution. The approach is to treat any well-isolated dot as if it were connected to neighboring dots by springs, and to move it to a location where the energy in the springs is a minimum. Applied to the whole image, this could degrade the halftone appearance. However, Springs only moves dots in selected regions of the image. To select these regions, Springs employs a segmentation scheme which is based on finding light regions which do not exhibit strong edge structures.

We exploit the techniques of tree structured vector quantization (TSVQ), branch and bound search, and the triangle inequality to speed the search of large image databases. Our method can reduce search computation required to locate images which best match a query image provided by a user. While exact search is possible, a free parameter allows search accuracy to be reduced, thereby providing a substantially better speed-up versus accuracy tradeoff.

We introduce a new approach that we call sequential linear interpolation (SLI) for approximating multidimensional nonlinear functions. The SLI is a partially separable grid structure that allows us to allocate more grid points to the regions where the function to be interpolated is more nonlinear. This approach reduces the mean squared error (MSE) between the original and approximated function while retaining much of the computational advantage of the conventional uniform grid interpolation. To obtain the optimal grid point placement for the SLI structure, we appeal to an asymptotic analysis similar to the asymptotic vector quantization (VQ) theory. In the asymptotic analysis, we assume that the number of interpolation grid points is large and the function to be interpolated is smooth. Closed form expressions for the MSE of the interpolation are obtained from the asymptotic analysis. These expressions are used to guide us in designing the optimal SLI structure. For cases where the assumptions underlying the asymptotic theory are not satisfied, we develop a postprocessing technique to improve the MSE performance of the SLI structure. The SLI technique is applied to the problem of color printer characterization where a highly nonlinear multidimensional function must be efficiently approximated. Our experimental results show that the appropriately designed SLI structure can greatly improve the MSE performance over the conventional uniform grid.

The theory of optimal stack filtering has been used in the difference of estimates (DoE) approach to the detection of intensity edges in noisy images. The DoE approach is modified by imposing a symmetry condition on the data used to train the two stack filters. Under this condition, the stack filters obtained are duals of each other. Only one filter must therefore be trained; the other is simply its dual. This new technique is called the symmetric difference of estimates (SDoE) approach. The dual stack filters obtained under the SDoE approach are shown to be comparable. This allows the difference of these two filters to be represented by a single equivalent edge operator. This latter result suggests that an edge operator can be found by directly training a (possibly nonpositive) Boolean function to be used on each level of the threshold decomposition architecture. This approach, which is called the threshold Boolean filter (TBF) approach, requires less training time but produces operators that are less robust than those produced by the SDoE approach. This is demonstrated and interpreted via comparisons of results for natural images.

A certain class of Markov random fields (MRF) known as generalized Gaussian MRFs (GGMRF) have been shown to yield good performance in modeling the a priori information in Bayesian image reconstruction and restoration problems. Though the ML estimate of temperature T of a GGMRF has a closed form solution, the optimal estimation of the shape parameter p is a difficult problem due to the intractable nature of the partition function. We present a tractable scheme for ML estimation of p by an off-line numerical computation of the log of the partition function. In image reconstruction or restoration problems, the image itself is not known. To address this problem, we use the EM algorithm to compute the estimates directly from the data. For efficient computation of the expectation step, we propose a fast simulation technique and a method to extrapolate the estimates when the simulations are terminated prematurely prior to convergence. Experimental results show that the proposed methods result in substantial savings in computation and superior quality images.

We are developing a new graduate program at Purdue in Video and Image Systems Engineering (VISE). The project is comprised of three parts: a new curriculum centered around a degree option in VISE to be earned as part of the Masters or Ph.D. degrees; a state-of-the-art lecture/laboratory facility for instruction, laboratory experiments, and project and homework activities in VISE courses; and enhancement of existing courses and development of new courses in the VISE area.

The popularity of Bayesian methods in image processing applications has generated great interest in image modeling. A good image model needs to be non-homogeneous to be able to adapt to the local characteristics of the different regions in an image. In the past however, such a formulation was difficult since it was not clear as to how to choose the parameters of the non-homogeneous model. But now motivated by results in maximum likelihood parameter estimation of MRF models, we formulate in this paper a non-homogeneous Markov random field (MRF) image model in the multiresolution framework. The advantage of the multiresolution framework is two fold: first, it makes it possible to estimate the parameters of the nonhomogeneous MRF at any resolution by using the image at the coarser resolution. Second, it yields multiresolution algorithms which are computationally efficient and more robust than their single resolution counterparts. Experimental results in tomographic image reconstruction and optical flow computation problems verify the superior modeling provided by the new model.

Statistical tomographic reconstruction algorithms generally require the efficient optimization of a functional. An algorithm known as iterative coordinate descent with Newton-Raphson updates (ICD/NR) has been shown to be much more computationally efficient than indirect optimization approaches based on the EM algorithm. However, while the ICD/NR algorithm has experimentally been shown to converge stably, no theoretical proof of convergence is known. We prove that a modified algorithm, which we call ICD functional substitution (ICD/FS), has guaranteed global convergence in addition to the computational efficiency of the ICD/NR. The ICD/FS method works by approximating the log likelihood at each pixel by an alternative quadratic functional. Experimental results show that the convergence speed of the globally convergent algorithm is nearly identical to that of ICD/NR.

Visual assembly inspection can provide a low cost, accurate, and efficient solution to the automated assembly inspection problem, which is a crucial component of any automated assembly manufacturing process. The performance of such an inspection system is heavily dependent on the placement of the camera and light source. This article presents new algorithms that use the CAD model of a finished assembly for placing the camera and light source to optimize the performance of an automated assembly inspection algorithm. This general-purpose algorithm utilizes the component material properties and the contact information from the CAD model of the assembly, along with standard computer graphics hardware and physically accurate lighting models, to determine the effects of camera and light source placement on the performance of an inspection algorithm. The effectiveness of the algorithms is illustrated on a typical mechanical assembly.

Over the past years there has been considerable interest in statistically optimal reconstruction of cross-sectional images from tomographic data. In particular, a variety of such algorithms have been proposed for maximum a posteriori (MAP) reconstruction from emission tomographic data. While MAP estimation requires the solution of an optimization problem, most existing reconstruction algorithms take an indirect approach based on the expectation maximization (EM) algorithm. We propose a new approach to statistically optimal image reconstruction based on direct optimization of the MAP criterion. The key to this direct optimization approach is greedy pixel-wise computations known as iterative coordinate decent (ICD). We propose a novel method for computing the ICD updates, which we call ICD/Newton-Raphson. We show that ICD/Newton-Raphson requires approximately the same amount of computation per iteration as EM-based approaches, but the new method converges much more rapidly (in our experiments, typically five to ten iterations). Other advantages of the ICD/Newton-Raphson method are that it is easily applied to MAP estimation of transmission tomograms, and typical convex constraints, such as positivity, are easily incorporated.

This paper describes the design of color filters for a surface color measurement device. The function of the device is to return the XYZ tristimulus vector characterizing the color of the surface. The device is designed to measure emissive as well as reflective surfaces. It uses an internal set of LEDs to illuminate reflective surfaces while characterizing their color under assumed standard illuminants. In the design of the filters, we formulate a nonlinear optimization problem with the goal of minimizing error in the uniform color space CIE L*a*b*. Our optimization criteria employs a technique to retain a linear structure while approximating the true L*a*b* error. In addition, our solution is regularized to account for system noise, filter roughness, and filter implementation errors. Experimental results indicate average and worst-case device accuracy of 0.27 L*a*b* DeltaE units and 1.56 L*a*b* DeltaE units for a "system tolerance" of 0.0005.

Bayesian methods have proven to be powerful tools for computed tomographic reconstruction in realistic physical problems. However, Bayesian methods require that a number of modeling and computational problems be addressed. The paper summarizes a coherent system of statistical modeling and optimization techniques designed to facilitate efficient, unsupervised Bayesian emission and transmission tomographic reconstruction. New results are included on improved convergence behavior of these methods.

While Bayesian methods can significantly improve the quality of tomographic reconstructions, they require the solution of large iterative optimization problems. Recent results indicate that the convergence of these optimization problems can be improved by using sequential pixel updates, or Gauss-Seidel iterations. However, Gauss-Seidel iterations may be perceived as less useful when parallel computing architectures are use. We show that for degrees of parallelism of typical practical interest, the Gauss-Seidel iterations updates may be computed in parallel with little loss in convergence speed. In this case, the theoretical speed up of parallel implementations is nearly linear with the number of processors.

Searching an image for the occurrence of a pattern or a template is an essential step in a number of image processing applications. We propose a new multiresolution matching criterion based on the generalized log likelihood ratio. We also developed a multiscale search technique which facilitates finding the best solution by searching a small subset of the entire set of possible template locations. The search technique is designed to keep the amount of computation at each resolution approximately the same. The results obtained on our example images demonstrate the robustness and accuracy of the matching criterion along with a speed-up of over two orders of magnitude by the search technique.

This paper describes the design of color filters for a surface color measurement device. The function of the device is to return the XYZ tristimulus vector characterizing the color of the surface. The device is designed to measure emissive as well as reflective surfaces. It uses an internal set of LEDs to illuminate reflective surfaces while characterizing their color under assumed standard illuminants. In the design of the filters, we formulate a nonlinear optimization problem with the goal of minimizing error in the uniform color space CIE L*a*b*. Our optimization criteria employs a technique to retain a linear structure while approximating the true L*a*b* error. In addition, our solution is regularized to account for system noise, filter roughness and filter implementation errors. Experimental results indicate average and worst case device accuracy of 0.27 L*a*b* /spl Delta/E units and 1.56 L*a*b* /spl Delta/E units for a "system tolerance" of 0.0005.

Proposes an efficient vector quantization (VQ) technique called sequential scalar quantization (SSQ). The scalar components of the vector are individually quantized in a sequence, with the quantization of each component utilizing conditional information from the quantization of previous components. Unlike conventional independent scalar quantization (ISQ), SSQ has the ability to exploit intercomponent correlation. At the same time, since quantization is performed on scalar rather than vector variables, SSQ offers a significant computational advantage over conventional VQ techniques and is easily amenable to a hardware implementation. In order to analyze the performance of SSQ, the authors appeal to asymptotic quantization theory, where the codebook size is assumed to be large. Closed-form expressions are derived for the quantizer mean squared error (MSE). These expressions are used to compare the asymptotic performance of SSQ with other VQ techniques. The authors also demonstrate the use of asymptotic theory in designing SSQ for a practical application (color image quantization), where the codebook size is typically small. Theoretical and experimental results show that SSQ far outperforms ISQ with respect to MSE while offering a considerable reduction in computation over conventional VQ at the expense of a moderate increase in MSE.

Multispectral images are composed of a series of images at differing optical wavelengths. Since these images can be quite large, they invite efficient source coding schemes for reducing storage and transmission requirements. Because multispectral images include a third (spectral) dimension with nonstationary behavior, these multilayer data sets require specialized coding techniques. The authors develop both a theory and specific methods for performing optimal transform coding of multispectral images. The theory is based on the assumption that a multispectral image may be modeled as a set of jointly stationary Gaussian random processes. Therefore, the methods may be applied to any multilayer data set which meets this assumption. Although the authors do not assume the autocorrelation has a separable form, they show that the optimal transform for coding has a partially separable structure. In particular, they prove that a coding scheme consisting of a frequency transform within each layer followed by a separate KL transform across the layers at each spatial frequency is asymptotically optimal as the block size becomes large. Two simplifications of this method are also shown to be asymptotically optimal if the data can be assumed to satisfy additional constraints. The proposed coding techniques are then implemented using subband filtering methods, and the various algorithms are tested on multispectral images to determine their relative performance characteristics.

In this paper, we develop a novel multiscale stochastic image model to describe the appearance of a complex threedimensional object in a two-dimensional monochrome image.This formal image model is used in conjunction with Bayesian estimation techniques to perform automated inspection.The model is based on a stochastic tree structure in which each node is an important subassembly of the three-dimensional object.The data associated with each node or subassembly is modeled in a wavelet domain.We use a fast multiscale search technique to compute the sequential MAP (SMAP) estimate of the unknown position, scale factor, and 2-D rotation for each subassembly.The search is carried out in a manner similar to a sequential likelihood ratio test, where the process advances in scale rather than time.The results of this search determine whether or not the object passes inspection.A similar search is used in conjunction with the EM algorithm to estimate the model parameters for a given object from a set of training images.The performance of the algorithm is demonstrated on two different real assemblies. I. INTRODUCTIONF ORMAL mathematical image models have long been used in the design of image processing algorithms for applications such as compression, restoration, and enhancement [1].Such models are traditionally low level stochastic models of limited complexity.In recent years, however, important theoretical advances and increasingly powerful computers have led to more complex and sophisticated image models.Depending on the application, researchers have proposed both low-level and high-level models.Low-level image models describe the behavior of individual image pixels relative to one another.Markov random fields and other spatial interaction models have proven useful for a variety of applications, including image segmentation and restoration [2]; [3].Bouman and Shapiro [4], along with Willsky, Benveniste, and their associates [5], [6], have developed multiscale stochastic models for image data.High-level models are generally used to describe a more restrictive class of images.These models describe larger struc-

The new approach to undergraduate DSP education at Purdue is based on a simple idea: emphasize applications. Students are assumed to have a significant exposure to sampling and discrete-time signals, systems, and transforms at the junior level. In the senior course, the traditional DSP topics of digital filter design, the DFT, radix-2 FFT's, and quantization are covered in the first five weeks of the semester. Coverage of these topics is augmented by treatment in the laboratory component of the course using diverse software tools and by Matlab based homework assignments. The remainder of the course is devoted to treating the topics of speech processing and image processing in substantial depth and involves a design project. The course has been very successful in terms of increasing enrolment and outstanding student evaluations.>

This paper presents the exact maximum likelihood (ML) estimate of temperature for a class of Markov random fields (MRF) known as generalized Gaussian MRFs. The ML estimate has a simple closed form which is analogous to variance estimation for Gaussian random variables. This result is useful because the temperature parameter plays the important role of determining the amount of smoothing in problems such as Bayesian image reconstruction and restoration. Two extensions of the basic result are also given: 1) numerical scale estimation for the general class of continuous MRFs; and 2) parameter estimation from incomplete data using the EM algorithm. Preliminary numerical experiments support the usefulness of the technique.>

In this paper we develop a general multiscale stochastic object detection algorithm for use in an automated inspection application. Information from a CAD model is used to initialize the object model and guide the training phase of the algorithm. An object is represented as a stochastic tree, where each node of the tree is associated with one of the various object components used to locate and identify the part. During the training phase a number of model parameters are estimated from a set of training images, some of which are generated from the CAD model. The algorithm then uses a fast multiscale search strategy to locate and identify the subassemblies making up the object tree. We demonstrate the performance of the algorithm on a typical mechanical assembly.>

Introduces a new approach which we call sequential linear interpolation (SLI) for interpolating multidimensional nonlinear functions. SLI grid points can be nonuniformly placed. By applying asymptotic analysis, we obtain optimal conditions for placing the interpolation grid points in the SLI grid structure to minimize the interpolation error. Thus, we use the grid points more efficiently. We apply this technique to the color printer calibration problem where highly nonlinear functions must be efficiently implemented.>

Bayesian reconstruction and restoration methods require the choice of parameters related to variance in both stochastic image models and observed data. In practice these parameters, or their ratio, is often chosen heuristically. The authors present a method for joint maximum-likelihood (ML) estimation of these two parameters in transmission tomography, with emphasis on the X-ray//spl gamma/-ray dosage parameter. The estimation algorithm employs the expectation-maximization method, with the unobserved image as the complete data. The ML parameter estimator is shown to yield values which are practical for tomographic reconstruction, both with synthetic phantoms and real data.>

An important part of a robust automated assembly process is an accurate and efficient method for the inspection of finished assemblies. This paper presents a novel multiscale assembly inspection algorithm that is used to detect errors in an assembled product. The algorithm is trained on synthetic images generated using the CAD model of the different components of the assembly. The CAD model guides the inspection algorithm through its training stage by addressing the different types of variations that occur during manufacturing and assembly. Those variations are classified into those that can affect the functionality of the assembled product and those that are unrelated to its functionality. Using synthetic images in the training process adds to the versatility of the technique by removing the need to manufacture multiple prototypes and control the lighting conditions. Once trained on synthetic images, the algorithm can detect assembly errors by examining real images of the assembled product. The effectiveness of the system is illustrated on a typical mechanical assembly.>

Many approaches to Bayesian image segmentation have used maximum a posteriori (MAP) estimation in conjunction with Markov random fields (MRF). Although this approach performs well, it has a number of disadvantages. In particular, exact MAP estimates cannot be computed, approximate MAP estimates are computationally expensive to compute, and unsupervised parameter estimation of the MRF is difficult. The authors propose a new approach to Bayesian image segmentation that directly addresses these problems. The new method replaces the MRF model with a novel multiscale random field (MSRF) and replaces the MAP estimator with a sequential MAP (SMAP) estimator derived from a novel estimation criteria. Together, the proposed estimator and model result in a segmentation algorithm that is not iterative and can be computed in time proportional to MN where M is the number of classes and N is the number of pixels. The also develop a computationally efficient method for unsupervised estimation of model parameters. Simulations on synthetic images indicate that the new algorithm performs better and requires much less computation than MAP estimation using simulated annealing. The algorithm is also found to improve classification accuracy when applied to the segmentation of multispectral remotely sensed images with ground truth data.

We present a method for object detection based on a novel multiscale stochastic model together with Bayesian estimation techniques. This approach results in a fast, general algorithm which may be easily trained for specific objects. The object model is based on a stochastic tree structure in which each node is an important subassembly of the three dimensional object. Each node or subassembly is modeled using a Gaussian pyramid decomposition. The objective of the algorithm is then to estimate the unknown position of each subassembly, and to determine on the presence of the object. We use a fast multiscale search technique to compute the sequential MAP (SMAP) estimate of the unknown position, scale factor, and 2-D rotation for each subassembly. The search is carried out in a manner similar to a sequential likelihood ratio test, where the process advances in scale rather than time. We use a similar search to estimate the model parameters for a given object from a set of training images.

The authors present a Markov random field model which allows realistic edge modeling while providing stable maximum a posterior (MAP) solutions. The model, referred to as a generalized Gaussian Markov random field (GGMRF), is named for its similarity to the generalized Gaussian distribution used in robust detection and estimation. The model satisfies several desirable analytical and computational properties for map estimation, including continuous dependence of the estimate on the data, invariance of the character of solutions to scaling of data, and a solution which lies at the unique global minimum of the a posteriori log-likelihood function. The GGMRF is demonstrated to be useful for image reconstruction in low-dosage transmission tomography.

A new approach to Bayesian image segmentation based on a novel multiscale random field (MSRF) and a new estimation approach called sequential maximum a posteriori estimation are presented. Together, the proposed estimator and model result in a segmentation algorithm which is not iterative and can be computed in time proportional to MN where M is the number of classes and N is the number of pixels. A method for estimating the parameters of the multiscale model directly from the image during the segmentation process is developed.>

A method is presented for Bayesian reconstruction from projections which updates single pixel values, rather than the entire image, at each step. The technique is similar to Gauss-Seidel (GS) iteration for the solution of differential equations on finite grids. The computational cost per iteration of the GS approach is found to be approximately equal to that of gradient methods. For continuously valued images, GS is found to have significantly better convergence at modes representing high spatial frequencies. In addition, GS is well-suited to segmentation when the image is constrained to be discrete-valued.>

A multiple resolution algorithm is presented for segmenting images into regions with differing statistical behavior. In addition, an algorithm is developed for determining the number of statistically distinct regions in an image and estimating the parameters of those regions. Both algorithms use a causal Gaussian autoregressive model to describe the mean, variance, and spatial correlation of the image textures. Together, the algorithms can be used to perform unsupervised texture segmentation. The multiple resolution segmentation algorithm first segments images at coarse resolution and then progresses to finer resolutions until individual pixels are classified. This method results in accurate segmentations and requires significantly less computation than some previously known methods. The field containing the classification of each pixel in the image is modeled as a Markov random field. Segmentation at each resolution is then performed by maximizing the a posteriori probability of this field subject to the resolution constraint. At each resolution, the a posteriori probability is maximized by a deterministic greedy algorithm which iteratively chooses the classification of individual pixels or pixel blocks. The unsupervised parameter estimation algorithm determines both the number of textures and their parameters by minimizing a global criterion based on the AIC information criterion. Clusters corresponding to the individual textures are formed by alternately estimating the cluster parameters and repartitioning the data into those clusters. Concurrently, the number of distinct textures is estimated by combining clusters until a minimum of the criterion is reached.>

A method of estimating both the number and type of textures in an image is proposed. An autoregressive (AR) texture model is used since it describes spatial behavior in addition to mean and local variation. Solution criteria are formulated based on the concurrent estimation of the number of textures, the texture parameters, and the class of texture samples. This approach avoids problems with the instability of maximum likelihood estimation and results in an algorithm which is composed of three basic operations. The first two operations alternately reestimate the texture parameters and repartition the data into the clusters corresponding to individual textures. The third operation agglomerates clusters to reduce the number of distinct textures. Each operation attempts to minimize the basic solution criteria.>

A method is presented for segmenting images into a discrete set of classes by first segmenting at low resolution and then progressing to finer resolutions until individual pixels are classified. This multiple resolution method results in accurate segmentations and requires significantly less computation than some previously known methods. The segmentation algorithm used at each resolution is based on maximum a posteriori estimation of the field of pixel classifications, which is modeled as a Markov random field. The maximization is performed by a deterministic greedy algorithm which iteratively chooses the classification of individual pixels or blocks of pixels. A texture model is also developed which allows the extraction of a texture statistic for each pixel and is well suited for use with the proposed algorithm. Measurements of algorithm performance under varying conditions of region size and signal-to-noise ratio are presented.>

A direct-sequence spread-spectrum packet radio is described that has versatile signal-processing and local-control capabilities designed to support the functions required of a robust mobile communications network. Noteworthy capabilities include eleven selectable data rates with accurate range measurements in a fading multipath channel. The radio uses a hybrid analog/digital signal processor and nonrepeating spreading codes for suppression of intersymbol interference and jamming. It incorporates two sets of monolithic surface-acoustic-wave convolvers as programmable matched filters with time-bandwidth products of 64 and 2000. The analog matched filters are coupled with binary postprocessing for the functions of detection, RAKE demodulations and ranging measurements over a wide multipath spread. The data rate can be varied in response to channel conditions from 1.45 Mb/s down to 44 b/s with an almost ideal tradeoff in signal-processing gain from 18 dB up to 61 dB prior to multipath combining.>

Advances in signal processing and architectural design for high-performance packet radio are described. The scope of the work roughly encompasses the data-link and physical levels of standardized layered-network architectures. A hardware-function layering approach is used, including the purposeful design of an interface to provide a structured control environment for a demonstration packet radio. The advanced signal processing provides a robust, flexible data link to service demanding network environments, and uses 100-MHz-bandwidth surface-acoustic-wave (SAW) convolvers as large time-bandwidth product matched filters for communication with nonrepeating pseudonoise waveforms. The convolvers are combined with a binary-quantized postprocessor to implement a hybrid correlator which provides high processing gain for detection, demodulation, and ranging measurements. Data rates can be selected, in response to varying channel conditions, over a range from 1.45 Mbits/s down to 44 bits/s with an almost ideal tradeoff in processing gain for interference rejection and privacy ranging from 18 dB up to 61 dB. Future enhancements are proposed that will advance both the signal processing and the architecture.