Multi-spectral imaging is pivotal in numerous industrial, scientific, and medical fields, yet existing high-resolution systems often rely either on bulky prototypes or costly handheld setups. This paper introduces a novel approach to spectral imaging using a cost-effective handheld camera: the Spectral Camera (SpectralCam). It leverages the advanced optics, sensors, and electronics of a standard Canon EOS R100 DSLR (digital single-lens reflex) camera along with a composite 12-color, color-coded aperture (CCA) fabricated with Fuji Velvia 50 film to enhance light polarization into the DSLR. Additionally, we train a denoising diffusion probabilistic model (DDPM) and devise a guided diffusion workflow to reconstruct images across 12 and 24 spectral bands ranging from 430 to 660 nanometers. Notably, our method eliminates the need for application or hardware-specific training by leveraging the capability of generative artificial intelligence (AI), thus allowing for flexible adaptation to various experimental setups. The proposed solution demonstrates the potential to address diverse challenges in multi-spectral imaging by achieving high-resolution spectral data capture, improved adaptability and deployability while significantly reducing costs and complexity.

Hypergraph neural networks have been promising tools for handling learning tasks involving higher-order data, with notable applications in web graphs, such as modeling multi-way hyperlink structures and complex user interactions. Yet, their generalization abilities in theory are less clear to us. In this paper, we seek to develop margin-based generalization bounds for four representative classes of hypergraph neural networks, including convolutional-based methods (UniGCN), set-based aggregation (AllDeepSets), invariant and equivariant transformations (M-IGN), and tensor-based approaches (T-MPHN). Through the PAC-Bayes framework, our results reveal the manner in which hypergraph structure and spectral norms of the learned weights can affect the generalization bounds, where the key technical challenge lies in developing new perturbation analysis for hypergraph neural networks, which offers a rigorous understanding of how variations in the model's weights and hypergraph structure impact its generalization behavior. Our empirical study examines the relationship between the practical performance and theoretical bounds of the models over synthetic and real-world datasets. One of our primary observations is the strong correlation between the theoretical bounds and empirical loss, with statistically significant consistency in most cases.

Sensing the Earth’s surface topography and vegetation (STV) structure is of critical importance for a myriad of scientific applications. STV metrology relies on lidar, radar, stereophotogrammetry, or a combination of these remote sensing techniques. STV metrology, however, suffers from low spatial and height resolution or sparse coverage if lidars and stereophotogrammetry are deployed at orbital heights. Many scientific applications such as bare Earth, cryosphere, and hydrology, require meter or sub-meter STV observables in spatial resolution with submeter vertical resolution. This work aims to overcome the STV resolution gap by using a simple observation system composed of an orbital Compressive Sensing (CS) lidar aided by high-resolution monocular RGB photography. The system first produces a super-resolved digital surface model by fusing satellite CS lidar photon returns with monocular photography using an image-to-image translation generative Brownian Bridge Diffusion Model. Subsequently, the low photon count lidar measurements together with the high-resolution DSM are then used in a constrained Denoising Diffusion Probabilistic Model to reconstruct super-resolved, wall-to-wall, and feature-rich HyperHeight STV Data Cubes. This approach effectively enhances the resolution for satellite LiDAR imagery while reducing generative model hallucinations, thereby improving the reliability and utility of the resulting data products for Earth studies. The achievable spatial resolution depends on the monocular RGB imagery resolution, the photon density of the training point cloud, and the noise level in the LiDAR sensor.

Spaceborne lidars are essential for monitoring Earth’s ecosystems, particularly in imaging forests, glaciers, and natural hazards. However, current satellite lidar systems, such as NASA’s Global Ecosystem Dynamics Investigation (GEDI) and Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2), are limited in spatial resolution and photon density, constraining their ability to capture detailed surface topography and vegetation (STV) 3-D imagery. Airborne systems, such as NASA’s G-LiHT, offer higher resolution but lack global coverage. To address these limitations, compressive satellite lidars (CS-Lidars) have been recently introduced, utilizing coded laser illumination and dynamic wavelength scanning for wide-field 3-D imaging. A novel framework, based on hyperheight data cubes (HHDCs), uses deep learning to transform sparse measurements into 3-D images, but its resolution remains constrained by the physical limitations of the instruments. This article proposes three approaches using generative diffusion models to achieve super-resolution lidar imaging, enhancing satellite data resolution. These methods involve learning conditional probabilities, guiding models via forward imaging, and leveraging high-resolution side information. The results show substantial improvements in the resolution of satellite lidar data, enabling fine-scale studies of forest structure and improving applications in forest management and environmental monitoring. The methodologies were tested in three regions of USA: Florida, Maryland, and California. The models were trained and tested on the first two, and their zero-shot capabilities were tested on the third, showing comparable results.

Hypergraph neural networks (HyperGNNs) are a family of deep neural networks designed to perform inference on hypergraphs. HyperGNNs follow either a spectral or a spatial approach, in which a convolution or message-passing operation is conducted based on a hypergraph algebraic descriptor. While many HyperGNNs have been proposed and achieved state-of-the-art performance on broad applications, there have been limited attempts at exploring high-dimensional hypergraph descriptors (tensors) and joint node interactions carried by hyperedges. In this article, we depart from hypergraph matrix representations and present a new tensor-HyperGNN (T-HyperGNN) framework with cross-node interactions (CNIs). The T-HyperGNN framework consists of T-spectral convolution, T-spatial convolution, and T-message-passing HyperGNNs (T-MPHN). The T-spectral convolution HyperGNN is defined under the t-product algebra that closely connects to the spectral space. To improve computational efficiency for large hypergraphs, we localize the T-spectral convolution approach to formulate the T-spatial convolution and further devise a novel tensor-message-passing algorithm for practical implementation by studying a compressed adjacency tensor representation. Compared to the state-of-the-art approaches, our T-HyperGNNs preserve intrinsic high-order network structures without any hypergraph reduction and model the joint effects of nodes through a CNI layer. These advantages of our T-HyperGNNs are demonstrated in a wide range of real-world hypergraph datasets. The implementation code is available at https://github.com/wangfuli/T-HyperGNNs.git.

Compressive satellite LiDAR (CS-LiDAR) has been recently introduced as a radically different computational sensing and reconstruction approach for LiDAR sensing of Earth. It is based on NASA’s adaptive wavelength scanning LiDAR (AWSL) system. Unlike conventional 1D LiDAR methods, CS-LiDAR utilizes sparse coded laser illumination across a 2D field-of-view. The aim is to compressively capture Earth from hundreds of kilometers above, enabling computational 3D imagery reconstruction with resolution that is comparable to that attained with data collected from just hundreds of meters. The forward imaging model captures the light propagation phenomena affecting the photon pulses transmitted from the sensor to the Earth’s surface and back. This work enhances CS-LiDAR by integrating imaging spectroscopy into a multimodal system and employing a transformer network for the inverse imaging problem, driven by multimodal attention mechanisms. Emulations enabled by enormous observational LiDAR data of Earth, available from NASA’s G-LiHT imaging observatory, highlight the efficacy of methods developed.

This paper proposes an algorithm to enhance the resolution of satellite lidar data using Generative Adversarial Networks (GANs) under the hyperheight data cube framework. A super-resolution algorithm based on adversarial training is applied to overcome the challenges of long-range satellite lidar systems. The algorithm generates high-resolution super-resolved outputs from low-resolution inputs, improving the quality of several lidar representations such as canopy height models and profiles. This approach not only advances lidar-based models but also facilitates sophisticated lidar data analysis for various fields, such as environmental science, urban planning, and disaster management. The super-resolved lidar data provides a more precise depiction of the Earth's surface, opening up new avenues for research and applications in different domains. The framework's effectiveness was validated in the Florida Everglades National Park, where the resolution was increased from a 3m x 6m grid with 10m footprints to a 3m x 3m grid with 3m footprints, and the vertical resolution was enhanced from 0.5m to 0.25m.

Compressive satellite LiDAR (CS-LiDAR) has been recently introduced as a radically different computational sensing and reconstruction approach for LiDAR sensing of Earth. It is based on NASA’s adaptive wavelength scanning LiDAR (AWSL) system. Rather than measuring 1D line footprints over a satellite’s swath path as is the norm today, CS-LiDAR adopts sparse coded laser illumination over a 2D wide field-of-view. The objective is to compressively sense Earth from hundreds of km above Earth to then computationally reconstruct the 3D imagery with resolution and coverage as if the data was collected from just hundreds of meters in height. The forward imaging model captures the light propagation phenomena affecting the photon pulses transmitted from the sensor to the Earth’s surface and back. This paper advances CS-LiDAR on many fronts. First, imaging spectroscopy side-information, often jointly available with LiDARs, is integrated into a multimodal imaging system. Secondly, the inverse imaging problem is cast under a transformer network architecture driven by multimodal attention mechanisms. Finally, by directing the snapshot spectral cameras in front of the LiDAR, the transformer mechanisms autonomously adjust the LiDAR’s beam scanning to focus on specific target locations, thus attaining end-to-end optimal adaptive sampling that can respond to varying observational conditions, surface events, and scientific priorities. Emulations enabled by enormous observational LiDAR data of Earth, available from NASA’s G-LiHT imaging observatory, show the advantages attained by methods developed in this work.

LiDAR remote sensing systems are deployed in various platforms including satellites, airplanes, and drones — which, in essence, determines the sampling characteristics of the underlying imaging system. Low-altitude LiDARs provide high photon count and high spatial resolution but only in very localized patches. Satellite LiDARs, on the other hand, provide measurements at a global scale but are limited by low photon count and their samples are sparsely apart along swath line trajectories that are far in between. This paper describes a new class of satellite remote sensing LiDARs, aimed at overcoming the limitations of current satellite imaging systems. It exploits the principles of compressive sensing and machine learning (ML) to compressively sense Earth from hundreds of km above Earth to then reconstruct the 3D imagery with resolution and coverage, as if the data was collected from airborne platforms at just hundreds of meters in height.We introduce a novel representation of waveform altimetry profiles, coined HyperHeight Data Cubes (HHDC), which encompass rich information about the 3D structure of a scene. Canopy height models, digital terrain models, and many other features of a scene that are embedded in HHDC are easily extracted with simple statistical quantiles.We introduce machine learning methods to reconstruct the compressive LiDAR measurements so as to attain high-resolution, dense coverage, and broad field-of-view per swath pass. ML training data is attained from NASA’s G-LiHT imaging missions. Simulations with various types of forests across the US illustrate the power of the new LiDAR imaging systems.

Low-altitude airborne lidars deliver high spatial resolution swath mapping using dense laser footprint sampling but only in limited areas, while satellite lidars offer global sampling but are hampered by low resolution due to sparse footprints. This work presents a novel approach to satellite lidar remote sensing designed to address the low spatial resolution by leveraging the principles of compressive sensing and machine learning applied to a highly efficient, adaptive lidar capable of dense footprint sampling. Compressive sensing enables the distribution of footprints across a swath with a density appropriate to recover the features of interest, without unnecessarily oversampling the terrain. Machine learning techniques are employed to reconstruct the compressive lidar measurements, leading to high-resolution, dense coverage, and a broad field-of-view per swath pass. HyperHeight Data Cubes are introduced, which offer a wealth of information about the 3D structure of a scene, including digital surface models, canopy height models and the internal organization of canopies. Training data was obtained from NASA's G-LiHT airborne lidar, and simulations of satellite observations performed on various forest types across the US demonstrate the efficacy of the new lidar imaging approach.

Coded aperture snapshot spectral imager (CASSI) senses the spectral information of a 2-D scene and captures a set of coded measurement data that can be used to reconstruct the 3-D spatio-spectral datacube of the input scene by compressive sensing algorithms. The coded aperture (CA) in CASSI plays a crucial role in modulating the spatial information. The pixels in CA are typically square, switched binary ON–OFF, and aligned with the pixels of focal plane array (FPA). Instead of this binary modulation, this letter explores a simple yet effective approach to enabling an equivalent grayscale modulation, which can increase the sensing degree of freedom in CASSI systems. In particular, we deliberately introduce misalignment between the CA pixels and the FPA pixels, such that the spatial modulation of one FPA pixel is determined by four adjacent CA pixels instead of one. Numerical experiments show that the proposed equivalent grayscale modulation induced by misalignment can significantly improve the CASSI reconstruction when compared with current methods, whether a random CA or an optimal blue noise CA is used. More importantly, it does not incur in any cost to the CASSI system.

This paper introduces a unified framework for developing graph-based change detection algorithms in remote sensing, which is based on signal feasibility problems and variational inequalities. We argue that signal feasibility problems provide a natural way to frame the change detection problem, while variational inequalities, core elements of modern data science and signal processing methods, enable us to find efficient, stable, and reliable solutions to the proposed feasibility problems. We demonstrate the design of both semi-supervised and unsupervised change detection schemes from our perspective, establishing connections with graph Laplacian filtering and graph convolutional networks. In contrast to specialized methods that rely on composite objective functions with multiple penalty parameters, our approach greatly simplifies hyperparameter selection, as the hyperparameters are both bounded and can form convex combinations (i.e., they are non-negative and sum up to one). We evaluate our approach on various real heterogeneous and homogeneous datasets, demonstrating its capabilities compared to traditional and modern change detection methods. Additionally, our ablation studies confirm the consistency of our solutions under variations in the number of nodes and graph structure learning methods. We conclude by discussing the advantages, limitations, and promising future research directions, with connections to graph filtering, sampling set selection, and self-supervised learning. The source code to replicate the experiments and explore the approach further is available on GitHub at https://github.com/jfflorez/Exploiting-variational-inequalities-for-generalized-change-detection-on-graphs.git.

In this paper, we address the problem of sampling on graphs for change detection in large multi-spectral (MS) and synthetic aperture radar (SAR) images by proposing a graph-based data-driven framework. The main steps of the proposed approach are: (i) the segmentation of regions that enclose the change; (ii) the use of smoothness prior for learning a graph of the regions; (iii) the integration of blue-noise sampling (BN) in the change detection scheme. We validate our approach in 14 real cases of remote sensing according to quantitative analyses. The results confirm that using a structured sampling such as BN outperforms recent state-of-the-art methods in change detection for multimodal data.

Compressive X-ray tomosynthesis is an emerging technology that can be used for medical diagnosis, safety inspection and industrial non-destructive testing. Traditional compressive X-ray tomosynthesis uses sequential illumination to interrogate the object of interest, which generates non-overlapping projection measurements. However, when multiple X-ray sources emit simultaneously, the projections corresponding to different sources overlap creating multiplexed measurements. Such measurement strategy leads to a non-linear reconstruction problem. The reconstruction of the three-dimensional (3D) object from multiplexed projections is an important problem. This paper proposes a non-linear 3D reconstruction approach for compressive X-ray tomosynthesis, where a set of coding masks are used to generate structured illumination and reduce radiation dose. The effectiveness of the method is verified by simulation experiments. It is shown that the proposed approach can reconstruct high-quality images with just a few snapshots.

Compressive multispectral imaging systems comprise a new generation of spectral imagers that capture coded projections of a scene where spectral data cubes are reconstructed computationally. Separately, time-of-flight (ToF) cameras obtain 2D range images where each pixel records the distance from the camera sensor to the target surface. The demand for these imaging modalities is rapidly increasing, and thus, there is strong interest in developing new image sensors that can simultaneously acquire multispectral-color-and-depth imagery (MS+D) using a single aperture. Work in this path has been mainly developed via RGB+D imaging. However, in RGB+D, the multispectral image is limited to three spectral channels, and the imaging system often relies on two image sensors. We recently proposed a compressive MS+D imaging device that used a digital-micromirror-device, requiring a bulky double imaging-and-relay path. To overcome the bulkiness and other difficulties of our previous imaging system, this work presents a more-compact MS+D imaging device with snapshot capabilities. It provides better spectral sensing, relying on a static color-coded-aperture (CCA) and a ToF sensor. To guarantee good quality in the recovery, we develop an optimization method for CCA based-on blue-noise-multitoning, solved via the direct-binary-search algorithm. A testbed-setup is reported along with simulated and real experiments that demonstrate the MS+D capabilities of the proposed system over static and dynamic scenes.

Spectral computed tomography (SCT) is used to perform material characterization in 3D images, a feature that is not possible with conventional computed tomography (CT) systems. Currently, photon-counting detectors are used to obtain the energy binned images in SCT, however, these detectors are costly and the measured data have low signal to noise ratios. This paper presents a new approach for SCT which circumvents the limitations of current SCT systems. It combines conventional X-ray imaging systems with K-edge coded aperture masks. In this scheme, a particular filter pair is aligned with each X-ray beam in a multi-shot architecture, therefore obtaining compressive measurements in both the spectral and spatial domains. Then, the energy binned images are reconstructed using the alternating direction method of multipliers (ADMM) to solve a joint sparse and low-rank optimization problem that exploits the structure of the spectral data-cube. Simulations using coded fan-beam X-ray projections demonstrate the feasibility of the proposed approach.

Coded aperture compressive spectral imagers allow sensing a three-dimensional (3D) data cube by using two-dimensional (2D) projections of the coded and spectrally dispersed source. The traditional block-unblock coded apertures have been recently replaced by patterned optical filter arrays, allowing to modulate the spatial and spectral information. The real implementation of these patterned or "colored" coded apertures in terms of cost and complexity, directly depends on the number of filters to be used as well as the number of snapshots to be captured. This paper introduces a coded aperture optimization having in consideration these restrictions, the final design obtained is a moving colored coded aperture, which improves the reconstruction quality of the data cube and is physically implementable. Simulations show the accuracy and performance achieved with the proposed approach yielding up to 3 dB gain in PSNR over the current literature designs.

Recent advances in compressive spectral imagers have demonstrated the potential of spatio-spectral modulation (SSM) for improved reconstruction performance. Existing SSM techniques, however, use either a color filter array or a complex optical arrangement, both of which can only provide limited modulation bandwidth in the spectral dimension. This paper proposes a practical SSM method to help address the "missing cone" problem of chromo-tomography. A high-resolution binary coded aperture is used to modulate the dispersed images, which in the Fourier domain fulfills a 3D convolution of the probed spectrum with the aperture's wide spectrum. This spectrum spreading process facilitates the compressed sensing strategy determined by the Fourier Slice Theorem and we demonstrate the advantages of the proposed approach with numerical experiments.

Full waveform inversion (FWI) is a state-of-the-art method that has been used to estimate parameters of the Earth's subsurface. One of the main drawbacks of the FWI method is its high computational complexity in terms of both time and memory. This occurs because the inversion method is based on the computation of a gradient function that requires the forward (and backward) wave propagation of sources (and residuals) through the subsurface medium. Nowdays, seismic surveys are large scale problems and therefore the computation and storage in RAM memory of both wavefields is not feasible. Therefore, different strategies for the FWI method should be used. In this paper, we use two different implementation strategies that avoid allocating the full wavefields in RAMmemory. Instead, the wavefields are re-computed while at the same time the gradient function is obtained. The recomputation of the wavefields remains possible from a practical point of view since we use parallel architectures (GPUs). We show that the estimated velocity models obtained with all the strategies are similar. We also show that the RAM consumption decreases up to 80% for the proposed strategies in comparison with the strategy that requires storing the full wavefields.

Compressive spectral imaging (CSI) has demonstrated to be a feasible technique for capturing the 3D spatio spectral information of a scene through less measurements than the Nyquist rate. The coded aperture snapshot spectral imaging (CAS-SI) is an example of a CSI optical architecture, which has been proposed to work on the visible electromagnetic spectrum. Due to the rich information contained in the infrared spectrum, in this paper, we mathematically model and demonstrate the implementation of a broadband CASSI system covering the visible and the near infrared spectra between 448 nm to 1436 nm. Particularly, we developed a Digital Micromirror Device-based CSI system, which implements dual-band CS measurement processes of 3D spatio-spectral scenes.

Hyperspectral remote sensing often captures imagery where the spectral profiles of the spatial pixels are the result of the reflectance contribution of numerous materials. Spectral unmixing is then used to extract the collection of materials, or endmembers, contained in the measured spectra and a set of corresponding fractions that indicate the abundance of each material present at each pixel. This paper aims at developing a spectral unmixing algorithm directly from compressive measurements acquired using the coded-aperture snapshot spectral imaging (CASSI) system. The proposed method first uses the compressive measurements to find a sparse vector representation of each pixel in a 3-D dictionary formed by a 2-D wavelet basis and a known spectral library of endmembers. The sparse vector representation is estimated by solving a sparsity-constrained optimization problem using an algorithm based on the variable splitting augmented Lagrangian multipliers method. The performance of the proposed spectral unmixing method is improved by taking optimal CASSI compressive measurements obtained when optimal coded apertures are used in the optical system. The optimal coded apertures are designed such that the CASSI sensing matrix satisfies a restricted isometry property with high probability. Simulations with synthetic and real hyperspectral cubes illustrate the accuracy of the proposed unmixing method.

Summary form only given. The multi-shot Coded Aperture Snapshot Spectral Imaging system (CASSI) is an imaging architecture that senses the spectral imaging information of a 3D cube using a 2D focal plane array snapshot. Modeled as the summation of coded and shifted versions of different spectral voxels, the compressive CASSI measurements are difficult to be further compressed due to little correlation and redundancy. This paper is dedicated to retaining the correlations in the original data cube by an embedded transform coding on the compressive measurements. Through statistical modeling, the transformed measurements prove to be more approximate to the distribution of original spectral images than the compressive measurements. Meanwhile, bit-plane coding for the transformed measurements is applied by taking advantage of the known code aperture. The significant performance of this embedded coder on random compressive measurements is evaluated for different number of snapshots.

Compressive spectral imagers have gained popularity recently due to their ability to sense a three-dimensional (3D) data cube with just a few two dimensional (2D) coded aperture projection snapshots. The coded apertures are realized by digital micromirror devices (DMD) which often do not match the pitch resolution of the focal plane array (FPA). This paper introduces the forward model and associated reconstruction algorithm for such mismatched spectral imagers, without the loss of spectral and spatial resolution. Simulations show the improvements in the reconstructions achieved with the proposed approach yielding up to 12 dB gain in PSNR with respect to traditional.

Compressive spectral imaging captures the spatial and spectral information of a scene using a set of two-dimensional random projections. Compressed sensing reconstruction algorithms are then used to recover the underlying three-dimensional source. This work presents a new generation of devices that attain compressive spectral image measurements by means of a colored-patterned detector and a dispersive element. Simulations show that these new generation devices can recover spectral scenes with up to 5 dB gain in PSNR with respect to traditional Coded Aperture Snapshot Spectral Imaging (CASSI) systems.

Compressive spectral imaging (CSI) systems capture the 3D spatio-spectral information of a scene by measuring 2D focal plane array (FPA) coded projections. A reconstruction algorithm exploiting the sparsity of the signal is then used to recover the underlying hyperspectral scene. CSI systems use a set of binary coded apertures, commonly realized through photomasks, to modulate the spatial characteristics of the scene. The reconstruction image quality in CSI is determined by the design of a 2D coded aperture binary set which block or unblock light from the scene onto the detector. This work extends the framework of CSI by replacing the traditional block-unblock photomasks by colored coded apertures which modulate the source not only spatially but spectrally as well. Simulations show a significant improvement in the quality of spectral image reconstructions.

Coded Aperture Snapshot Spectral Imaging (CASSI) systems capture the spatial and spectral information of a scene by measuring 2D coded projections on a focal plane array (FPA). Compressed sensing reconstruction algorithms are then used to recover the underlying spectral data cube. The quality of the reconstructions in CASSI is determined by the design of a set of block-unblock coded apertures. In this work, the block-unblock coded apertures in CASSI are replaced by colored coded apertures. The Restricted Isometry Property (RIP) of the colored CASSI is developed and the structure of the colored coded apertures is designed such that the RIP is better satisfied. Simulations show significant gain in the quality of reconstructions for the optimized colored coded apertures over that attained by traditional block-unblock coded apertures.

A novel framework for music genre classification, namely the joint sparse low-rank representation (JSLRR) is proposed in order to: 1) smooth the noise in the test samples, and 2) identify the subspaces that the test samples lie onto. An efficient algorithm is proposed for obtaining the JSLRR and a novel classifier is developed, which is referred to as the JSLRR-based classifier. Special cases of the JSLRR-based classifier are the joint sparse representation-based classifier and the low-rank representation-based one. The performance of the three aforementioned classifiers is compared against that of the sparse representation-based classifier, the nearest subspace classifier, the support vector machines, and the nearest neighbor classifier for music genre classification on six manually annotated benchmark datasets. The best classification results reported here are comparable with or slightly superior than those obtained by the state-of-the-art music genre classification methods.

Traditional hyperspectral imaging sensors acquire high-dimensional data that are used for the discrimination of objects and features in a scene. Recently, a novel architecture known as the coded-aperture snapshot spectral imaging (CASSI) system has been developed for the acquisition of compressive spectral image data with just a few coded focal plane array measurements. This paper focuses on developing a classification approach with hyperspectral images directly from CASSI compressive measurements, without first reconstructing the full data cube. The proposed classification method uses the compressive measurements to find the sparse vector representation of the test pixel in a given training dictionary. The estimated sparse vector is obtained by solving a sparsity-constrained optimization problem and is then used to directly determine the class of the unknown pixel. The performance of the proposed classifier is improved by taking optimal CASSI compressive measurements obtained when optimal coded apertures are used in the optical system. The set of optimal coded apertures is designed such that the CASSI sensing matrix satisfies a restricted isometry property with high probability. Several simulations illustrate the performance of the proposed classifier using optimal coded apertures and the gain in the classification accuracy obtained over using traditional aperture codes in CASSI.

Compressive spectral imaging (CSI) senses the spatio-spectral information of a scene by measuring 2D coded projections on a focal plane array. A ℓ1-norm-based optimization algorithm is then used to recover the underlying discretized spectral image. The coded aperture snapshot spectral imager (CASSI) is an architecture realizing CSI where the reconstruction image quality relies on the design of a 2D set of binary coded apertures which block-unblock the light from the scene. This paper extends the compressive capabilities of CASSI by replacing the traditional blocking-unblocking coded apertures by a set of colored coded apertures. The colored coded apertures are optimized such that the number of projections is minimized while the quality of reconstruction is maximized. The optimal design of the colored coded apertures aims to better satisfy the restricted isometry property in CASSI. The optimal designs are compared with random colored coded aperture patterns and with the traditional blocking-unblocking coded apertures. Extensive simulations show the improvement in reconstruction PSNR attained by the optimal colored coded apertures designs.

This paper introduces the concept of QR images, an automatic method to embed QR codes into color images with bounded probability of detection error. These embeddings are compatible with standard decoding applications and can be applied to any color image with full area coverage. The QR information bits are encoded into the luminance values of the image, taking advantage of the immunity of QR readers against local luminance disturbances. To mitigate the visual distortion of the QR image, the algorithm utilizes halftoning masks for the selection of modified pixels and nonlinear programming techniques to locally optimize luminance levels. A tractable model for the probability of error is developed and models of the human visual system are considered in the quality metric used to optimize the luminance levels of the QR image. To minimize the processing time, the optimization techniques proposed to consider the mechanics of a common binarization method and are designed to be amenable for parallel implementations. Experimental results show the graceful degradation of the decoding rate and the perceptual quality as a function the embedding parameters. A visual comparison between the proposed and existing methods is presented.

Coded aperture snapshot spectral imaging systems (CASSI) measure the 3D spatio-spectral information of a scene using several compressive 2D focal plane array (FPA) snapshots. The image reconstruction algorithms utilized in CASSI use a first-order approximation of the underlying analog sensing phenomena. A calibration method is then used to compensate for the coarse approximation - an approach not well suited for multishot CASSI systems. This paper develops a more accurate computational model for CASSI which provides a higher quality of image reconstruction. Several simulations are shown to illustrate the performance improvement attained by the new model.

A new code aperture design framework for multiframe code aperture snapshot spectral imaging (CASSI) system is presented. It aims at the optimization of code aperture sets such that a group of compressive spectral measurements is constructed, each with information from a specific subset of bands. A matrix representation of CASSI is introduced that permits the optimization of spectrally selective code aperture sets. Furthermore, each code aperture set forms a matrix such that rank minimization is used to reduce the number of CASSI shots needed. Conditions for the code apertures are identified such that a restricted isometry property in the CASSI compressive measurements is satisfied with higher probability. Simulations show higher quality of spectral image reconstruction than that attained by systems using Hadamard or random code aperture sets.

Compressed sampling (CS) is a technique that enables signal reconstruction at sub-Nyquist sampling rate. A key problem in CS is how to design the sampling scheme. In this paper, we propose a novel sampling method for compressed image sampling, which exploits a priori information and uses a block-based strategy to improve image reconstruction. Our block-based sampling scheme assigns more samples to blocks with more high-frequency contents while making sure that important coefficients of each block are sampled. Simulation results show that our proposed method outperforms existing methods on both reconstruction quality and running time.

We propose a novel block-based image transmission system, which exploits the a prior information existing in the DCT domain of images and combines both linear and non-linear coding schemes accommodated to a block-based DCT domain compressed sampling method. An image is firstly divided into blocks and each block is separately sampled in DCT domain. Different coding schemes are used to transmit the samples based on their properties. With block-based strategy, each image block can be processed and transmitted separately, which reduces a lot of latency. Besides, an efficient system optimization algorithm is proposed by jointly optimizing the power allocation scheme and the transmission parameters to search for the maximum peak signal-to-noise ratio (PSNR) of the reconstructed image. Simulation results show that the proposed system provides a good performance with less latency.

The Restricted Isometry Property (RIP) is an important concept in compressed sensing. It is well known that many random matrices satisfy the RIP with high probability, whenever the entries of the random matrix have finite second order moment. Recent work in compressed sensing has shown that it is possible to do dimensionality reduction and signal reconstruction using Cauchy random projections. This suggests that the l1distance is preserved when one projects a set of data points from a high-dimensional space, to one of lower dimension with a random matrix which does not have finite variance. This paper generalizes this concept where it is shown that α-stable projections, which preserve the lαdistance, also satisfy a generalized RIP property and consequently reconstruction from α-stable projections is feasible.

This paper addresses the problem of video anomaly recovery from a sequence of spectrally compressed video frames. Analysis of anomalies occurring in both time and spectrum is important in video surveillance applications. We present a methodology for the recovery of anomalies such as moving objects and their spectral signatures from spectrally compressed video. The spectrally compressed video frames are obtained by using a Coded Aperture Snapshot Spectral Imaging (CASSI) system. The CASSI system encodes a 3-D data cube containing both 2-D spatial information and spectral information in a single 2-D measurement. In the proposed methodology, we use the spectrally compressed video as columns of a large data matrix Q. Principal Component Pursuit (PCP) is then used to decompose Q into the stationary background and a sparse matrix capturing the anomalies in the foreground. The sparse matrix is then used jointly with Q to recover the spectral information of the objects of interest. An example for the recovery of video anomalies in a 3-channel spectral video system (RGB) is presented.

Spectral imaging is of interest in many applications, including wide-area airborne surveillance, remote sensing, and tissue spectroscopy. Coded aperture spectral snapshot imaging (CASSI) provides an efficient mechanism to capture a 3D spectral cube with a single shot 2D measurement. CASSI uses a focal plane array (FPA) measurement of a spectrally dispersed, aperture coded, source. The spectral cube is then attained using a compressive sensing reconstruction algorithm. In this paper, we explore a new approach referred to as random convolution snapshot spectral imaging (RCSSI). It is based on FPA measurements of spectrally dispersed coherent sources that have been randomly convoluted by a spatial light modulator. The new method, based on the theory of compressive sensing via random convolutions, is shown to outperform traditional CASSI systems in terms of PSNR spectral image cube reconstructions.

Color visual cryptography (VC) encrypts a color secret message into n color halftone image shares. Previous methods in the literature show good results for black and white or gray scale VC schemes, however, they are not sufficient to be applied directly to color shares due to different color structures. Some methods for color visual cryptography are not satisfactory in terms of producing either meaningless shares or meaningful shares with low visual quality, leading to suspicion of encryption. This paper introduces the concept of visual information pixel (VIP) synchronization and error diffusion to attain a color visual cryptography encryption method that produces meaningful color shares with high visual quality. VIP synchronization retains the positions of pixels carrying visual information of original images throughout the color channels and error diffusion generates shares pleasant to human eyes. Comparisons with previous approaches show the superior performance of the new method.

Dimensionality reduction via linear random projections are used in numerous applications including data streaming, information retrieval, data mining, and compressive sensing (CS). While CS has traditionally relied on normal random projections, corresponding to ℓ2distance preservation, a large body of work has emerged for applications where ℓ1approximate distances may be preferred. Dimensionality reduction in ℓ1use Cauchy random projections that multiply the original data matrix B ∈ 葷D×nwith a Cauchy random matrix R ∈ 葷n×k(k « min(n,D)), resulting in a projected matrix C ∈ 葷D×k. This paper focuses on developing signal reconstruction algorithms from Cauchy random projections, where the large suite of reconstruction algorithms developed in compressive sensing perform poorly due to the lack of finite second-order statistics in the projections. In particular, a set of regularized coordinate-descent Myriad regression based reconstruction algorithms are developed using, both l0and Lorentzian norms as sparsity inducing terms. The l0-regularized algorithm shows superior performance to other standard approaches. Simulations illustrate and compare accuracy of reconstruction.

In this paper, we address the compressive sensing signal reconstruction problem by solving an ℓ0-regularized Least Absolute Deviation (LAD) regression problem. A coordinate descent algorithm is developed to solve this ℓ0-LAD optimization problem leading to a two-stage operation for signal estimation and basis selection. In the first stage, an estimation of the sparse signal is found by a weighted median operator acting on a shifted-and-scaled version of the measurement samples with weights taken from the entries of the projection matrix. The resultant estimated value is then passed to the second stage that tries to identify whether the corresponding entry is relevant or not. This stage is achieved by a hard threshold operator with adaptable thresholding parameter that is suitably tuned as the algorithm progresses.

Halftone visual cryptography (HVC) is a visual sharing scheme where a secret image is encoded into halftone shares taking meaningful visual information. In this paper, novel construction method of HVC based on an iterative halftoning method is proposed. The secret image is concurrently embedded into binary valued shares while these shares are halftoned by constrained iterative halftoning. The proposed method is able to generate halftone shares showing natural images with high image quality. Reconstructed secret images, obtained by stacking qualified shares together, does not suffer from cross interference of share images. Simulations are provided to show the effectiveness of our proposed method.

A new algorithm to build blue noise masks using centroidal Voronoi tessellations (CVT) and a variant of Lloyd's Algorithm is presented. The algorithm takes advantage of the optimality properties of CVTs and through a modified version of Lloyd's algorithm, achieves optimization of the stacked binary patterns that build the mask. A new ordering for binary pattern design is presented, as well as a new metric that allows the creation of quality profiles of the masks. The masks generated by this method are used to halftone sample images, and quality profiles are created. It is shown that CVT masks outperform masks created by DBS and VaC according to the new metric defined and thorough visual inspection of halftoned images.

Weighted median filters are increasingly being used in signal processing applications and thus fast implementations are of importance. This paper introduces a fast algorithm to compute the weighted median of N samples which has linear time and space complexity as opposed to O(N logN) which is the time complexity of traditional sorting algorithms. The proposed algorithm is based on Quickselect which is closely related to the well known Quicksort. We compare the runtime and the complexity to Floyd and Rivest's algorithm SELECT which to date has been the fastest median finding algorithm and show that our algorithm is up to 30% faster.

Resorting to the rich, psycho-physiologically grounded, properties of the slow temporal modulations of music recordings, a novel classifier ensemble is built, which applies discriminant sparse projections. More specifically, over complete dictionaries are learned and sparse coefficient vectors are extracted to optimally approximate the slow temporal modulations of the training music recordings. The sparse coefficient vectors are then projected to the principal subspaces of their within-class and between-class covariance matrices. Decisions are taken with respect to the minimum Euclidean distance from the class mean sparse coefficient vectors, which undergo the aforementioned projections. The application of majority voting to the decisions taken by 10 individual classifiers, which are trained on the 10 training folds defined by stratified 10-fold cross-validation on the GTZAN dataset, yields a music genre classification accuracy of 84.96% on average. The latter exceeds by 2.46% the highest accuracy previously reported without employing any sparse representations.

Motivated by psychophysiological investigations on the human auditory system, a bio-inspired two-dimensional auditory representation of music signals is exploited, that captures the slow temporal modulations. Although each recording is represented by a second-order tensor (i.e., a matrix), a third-order tensor is needed to represent a music corpus. Non-negative multilinear principal component analysis (NMPCA) is proposed for the unsupervised dimensionality reduction of the third-order tensors. The NMPCA maximizes the total tensor scatter while preserving the non-negativity of auditory representations. An algorithm for NMPCA is derived by exploiting the structure of the Grassmann manifold. The NMPCA is compared against three multilinear subspace analysis techniques, namely the non-negative tensor factorization, the high-order singular value decomposition, and the multilinear principal component analysis as well as their linear counterparts, i.e., the non-negative matrix factorization, the singular value decomposition, and the principal components analysis in extracting features that are subsequently classified by either support vector machine or nearest neighbor classifiers. Three different sets of experiments conducted on the GTZAN and the ISMIR2004 Genre datasets demonstrate the superiority of NMPCA against the aforementioned subspace analysis techniques in extracting more discriminating features, especially when the training set has small cardinality. The best classification accuracies reported in the paper exceed those obtained by the state-of-the-art music genre classification algorithms applied to both datasets.

Compressed sensing (CS) provides an efficient way to acquire and reconstruct natural images from a limited number of linear projection measurements leading to sub-Nyquist sampling rates. A key to the success of CS is the design of the measurement ensemble. This correspondence focuses on the design of a novel variable density sampling strategy, where the a priori information of the statistical distributions that natural images exhibit in the wavelet domain is exploited. The proposed variable density sampling has the following advantages: 1) the generation of the measurement ensemble is computationally efficient and requires less memory; 2) the necessary number of measurements for image reconstruction is reduced; 3) the proposed sampling method can be applied to several transform domains and leads to simple implementations. Extensive simulations show the effectiveness of the proposed sampling method.

This paper introduces a color visual cryptography encryption method that produces meaningful color shares via visual information pixel (VIP) synchronization and error diffusion halftoning. VIP synchronization retains the positions of pixels carrying visual information of original shares throughout the color channels and error diffusion generates shares pleasant to human eyes. Comparisons with previous approaches show the superior performance of the new method.

In this paper, a new framework for confocal microscopy based on the novel theory of compressive sensing is proposed. Unlike wide field microscopy or conventional parallel beam confocal imaging systems that use charge-coupled devices (CCD) as acquisition devices in addition to complex mechanical scanning system, the proposed compressive confocal microscopy is a kind of parallel beam confocal imaging system which exploits the rich theory of compressive sensing by using a single pixel detector and a digital micromirror device (DMD) to capture linear projections of the in-focus image. With the proposed system, confocal imaging of high optical sectioning ability can be achieved at sub-Nyquist sampling rates. Theoretical analysis, simulations and experimental results are shown to demonstrate the characteristics and potential of the proposed approach.

Halftone visual cryptography (HVC) enlarges the area of visual cryptography by the addition of digital halftoning techniques. In particular, in visual secret sharing schemes, a secret image can be encoded into halftone shares taking meaningful visual information. In this paper, HVC construction methods based on error diffusion are proposed. The secret image is concurrently embedded into binary valued shares while these shares are halftoned by error diffusion-the workhorse standard of halftoning algorithms. Error diffusion has low complexity and provides halftone shares with good image quality. A reconstructed secret image, obtained by stacking qualified shares together, does not suffer from cross interference of share images. Factors affecting the share image quality and the contrast of the reconstructed image are discussed. Simulation results show several illustrative examples.

The emerging theory of compressed sensing (CS) provides a univer sal signal detection approach for sparse signals at sub-Nyquist sampling rates. A small number of random projection measurements from the received analog signal would suffice to provide salient information for signal detection. However, the compressive measure ments are not efficient at gathering signal energy. In this paper, a set of detectors called subspace compressive detectors are proposed where a more efficient detection scheme can be constructed by exploiting the sparsity model of the underlying signal. Furthermore, we show that the signal sparsity model can be approximately estimated using reconstruction algorithms with very limited random measurements on the training signals. Based on the estimated signal sparsity model, an effective subspace random measurement matrix can be designed for unknown signal detection, which significantly reduces the necessary number of measurements. The performance of the subspace compressive detectors is analyzed. Simulation results show the effectiveness of the proposed subspace compressive detectors.

The introduction of the blue-noise spectra-high-frequency white noise with minimal energy at low frequencies-has had a profound impact on digital halftoning for binary display devices, such as inkjet printers, because it represents an optimal distribution of black and white pixels producing the illusion of a given shade of gray. The blue-noise model, however, does not directly translate to printing with multiple ink intensities. New multilevel printing and display technologies require the development of corresponding quantization algorithms for continuous tone images, namely multitoning. In order to define an optimal distribution of multitone pixels, this paper develops the theory and design of multitone, blue-noise dithering. Here, arbitrary multitone dot patterns are modeled as a layered superposition of stack-constrained binary patterns. Multitone blue-noise exhibits minimum energy at low frequencies and a staircase-like, ascending, spectral pattern at higher frequencies. The optimum spectral profile is described by a set of principal frequencies and amplitudes whose calculation requires the definition of a spectral coherence structure governing the interaction between patterns of dots of different intensities. Efficient algorithms for the generation of multitone, blue-noise dither patterns are also introduced.

The concept of Active Queue Management (AQM), broadly used in Internet Congestion Control, has been recently introduced to ad hoc wireless networks as a means to mitigate the severe TCP unfairness across flows. In particular, Neighborhood RED (NRED) has been proposed as an extension to the Random Early Detection (RED) mechanism with the goal of ensuring fair bandwidth allocation across flows in the networks. NRED provides improvements but suffers from limitations that can make its broad implementation difficult. This paper describes two fundamental principles governing neighborhood congestion among TCP flows in ad hoc wireless networks which are exploited to develop an improved control mechanism. The first principle indicates that the likelihood of the channel being captured by a node grows exponentially with the disparity between the node's channel utilization and the expected utilization level. The second principle indicates that traditional random packet marking in NRED leads to reduced fairness across flows, pointing to a simple dropping/marking strategy based on the concept of error diffusion where packet marks are spread apart as homogeneously as possible. The power of these fundamental principles is demonstrated in a Congestion Control scheme referred to as Neighborhood Diffusion Early Marking (NDEM) which results in a more efficient bandwidth distribution compared to NRED.

In this paper, ultrawideband (UWB) channel estimation based on the novel theory of compressive sensing (CS) is developed. The proposed approach relies on the fact that transmitting an ultra-short UWB pulse through a multipath channel leads to a received UWB signal that can be approximated by a linear combination of a few atoms from a pre-defined dictionary, yielding thus a sparse representation of the received signal. The CS reconstruction capabilities are exploited to recover the composite pulse-multipath channel from a reduced set of random projections using the matching pursuit algorithm. This reconstructed signal is subsequently used as a referent template in a correlator based detector. Extensive simulations show that for different propagation scenarios and UWB communication environments, the CS detector outperforms traditional correlators using just 1/3 of the sampling rate leading thus to a reduced use of analog-to-digital resources in the channel estimation stage.

The emerging theory of compressed sensing (CS) has led to the remarkable result that signals having a sparse representation in some known basis can be represented (with high probability) by a small sample set, taken from random projections of the signal. Notably, this sample set can be smaller than that required by the ubiquitous Nyquist sampling theorem. Much like the generalized Nyquist sampling theorem dictates that the sampling rate can be further reduced for the representation of bandlimited signals, this paper points to similar results for the sampling density in CS. In particular, it is shown that if additional spectral information of the underlying sparse signals is known, colored random projections can be used in CS in order to further reduce the number of measurements needed. Such a priori information is often available in signal processing applications and communications. Algorithms to design colored random projection vectors are developed. Further, an adaptive CS sampling method is developed for applications where non-uniform spectral characteristics of the signal are expected but are not known a priori.

This paper proposes a method of normalization of cDNA microarray data. This approach uses all gene data to estimate the normalization parameters and it obtains these parameters using an algorithm based on least absolute deviation (LAD) regression. This method normalizes iteratively each microarray set after the estimation of the normalization parameters which uses a LAD regression algorithm. The normalization method has a robust performance since it assumes that the errors between arrays follow a Laplacian distribution, leading to the mean absolute error minimization as a performance criterion to be achieved. The proposed normalization method was evaluated using three performance measures and they show that LAD based normalization method minimizes the errors and provides a more consistent replicated data spread with respect to a least square based method

The problem of multitoning emerges as the result of advances on printing technology that allow the reproduction of different shades of gray applying techniques like multiple inks, different ink concentration or various dot sizes. The end result is an improvement in the quality of the reproduction. While some algorithms used for binary halftoning have been extended to deal with multitoning with a certain success, there is room for further improvement in the quality of the resulting images. Faheem, Arce, and Lau proposed gray level separation as a way to improve the quality of multitone images generated through error diffusion. In this paper a new gray level separation scheme is proposed whose objective is to ensure that black, gray and white pixels are printed in blue-noise patterns. The new scheme is applied to error diffusion as well as to the well known DBS algorithm. The results in both cases show an improvement in the texture of the printed patterns.

This paper considers the problem of encoding a secret binary image SI into n shares of meaningful halftone images within the scheme of visual cryptography. We extend our previous work on halftone visual cryptography and propose a new method that can encode the secret pixels into the shares via simple error diffusion. The noise introduced by encoded secret pixels is totally diffused away to neighboring pixels and pleasing halftone shares can be achieved. The secret image can be clearly decoded without showing any interference with the share image. The security of our method is guaranteed by the properties of visual cryptography.

Virtual backbone structures are of fundamental importance in mobile ad hoc networks (MANET) as they are essential to support various applications such as service discovery and provision, multicast, routing, etc. In this paper we consider a very natural approach for the creation of virtual backbones, based on weakly-dominating sets, and investigate its security properties against Byzantine adversaries that can corrupt up to a given threshold of nodes. We formalize the notion of secure protocols for the creation and management of virtual backbones, and design a distributed protocol generating weakly-dominating virtual backbones, that is both efficient, according to standard MANET metrics, and secure against Byzantine adversaries corrupting up to a given threshold of nodes

Reliable server pooling (rSerPool) is an architecture and a set of protocols allowing a service provider to run several servers that can reliably provide the same service. Should a particular server fail while providing its service, another server can efficiently replace it. This property is attractive not only for wired but also for wireless networks. However, the unique characteristics of mobile ad hoc networks (MANETs) bring serious reliability and security challenges to the application of rSerPool. In this paper, we perform a comprehensive investigation of the security of rSerPool in MANET against both server failures and, especially, Byzantine attacks. We formulate security requirements for rSerPool in MANET and design efficient, distributed, and survivable security solutions for both main phases of rSerPool: service discovery and service provision. Specifically, we secure the service discovery phase by using a secure multiple-dominating set creation protocol, and the service provision phase by using a novel type of threshold signature scheme. Both protocols address novel security goals and are of independent interest as they can find applications to other areas; most notably, the construction of a distributed and survivable public-key infrastructure in MANET.

Approximate message authentication codes (AMACs) for binary alphabets have been introduced recently as noise-tolerant authenticators. Different from conventional “hard” message authentications that are designed to detect even the slightest changes in messages, AMACs are designed to tolerate a small amount of noise in messages for applications where slight noise is acceptable, such as in multimedia communications. Binary AMACs, however, have several limitations. First, they do not naturally deal with messages having$N$-ary alphabets$(N≫2)$. AMACs are distance-preserving codes; i.e., the distance between two authentication tags reflects the distance between two messages. Binary representation of$N$-ary alphabets, however, may destroy the original distance information between$N$-ary messages. Second, binary AMACs lack a means to adjust authentication sensitivity. Different applications may require different sensitivities against noise. AMACs for$N$-ary alphabets are designed as a cryptographic primitive to overcome the limitations of binary AMACs.$N$-ary AMACs not only directly process messages having$N$-ary alphabets but also provide sensitivity control on the authentication of binary and of$N$-ary messages. The generalized$N$-ary AMAC algorithm and its probabilistic model are developed. A statistical analysis characterizing the behavior of$N$-ary AMACs is provided along with the simulations illustrating their properties. Security analysis under chosen message attack is also developed.

Visual cryptography encodes a secret binary image (SI) into n shares of random binary patterns. If the shares are xeroxed onto transparencies, the secret image can be visually decoded by superimposing a qualified subset of transparencies, but no secret information can be obtained from the superposition of a forbidden subset. The binary patterns of the n shares, however, have no visual meaning and hinder the objectives of visual cryptography. Extended visual cryptography [1] was proposed recently to construct meaningful binary images as shares using hypergraph colourings, but the visual quality is poor. In this paper, a novel technique named halftone visual cryptography is proposed to achieve visual cryptography via halftoning. Based on the blue-noise dithering principles, the proposed method utilizes the void and cluster algorithm [2] to encode a secret binary image into n halftone shares (images) carrying significant visual information. The simulation shows that the visual quality of the obtained halftone shares are observably better than that attained by any available visual cryptography method known to date.

This paper introduces a multicarrier communication receiver for broadband applications based on analog to digital conversion (ADC) of the received signal in the frequency domain. The samples of the spectrum of the received signal are used in the digital receiver to estimate the transmitted symbols through a matched filter operation in the discrete frequency domain. The proposed receiver is aimed at the reception of high information rates in a multicarrier signal with very large bandwidth. Thus, the receiver architecture provides a solution to some of the challenging problems found in the implementation of conventional wideband multicarrier receivers based on time-domain ADC, since It efficiently parallelizes the A/D conversion reducing the sampling speed requirements. We show that the sampling rate requirements are relaxed as the number of frequency samples is increased, which introduces a trade-off between complexity and sampling rate. The new receiver possesses additional advantages, including scalability with increasing frequency samples, the possibility of optimally allocating the available number of bits for the ATD conversion across the frequency domain samples which potentially reduces the distortion introduced by the high-speed ADC, narrowband interference suppression that can be directly carried out in the frequency domain, and inherent robustness to frequency offset which makes it an attractive solution when compared with traditional multicarrier receivers. We also investigate how the proposed receiver responds to common multicarrier communication receiver problems such as phase noise and channel frequency selectivity.

This paper focuses on extending the weighted median for use with multidimensional (multichannel) signals. Sorting multicomponent (vector) values and selecting the middle value is not well defined as in the scalar case. This paper introduces two median based multivariate filtering structures inspired by ML estimates of location in multivariate spaces. Unlike Astola's weighted vector median filter, the multichannel weighted median filter structures introduced in this paper are able to exploit the spatial and cross-channel correlations embedded in the data. Adaptive optimization algorithms for the filters are derived. The effectiveness of these algorithms is shown through image and array processing experiments.

Active queue management (AQM) schemes proposed to date use control mechanisms having fundamental weaknesses often leading to overparameterization and instabilities. This paper draws from the rich theory of dithering and quantization, extensively used in signal processing, to develop new marking and control mechanisms that overcome such limitations. In particular, a packet marking mechanism is developed through error diffusion filtering where congestion is measured and controlled through the instantaneous queue, the derivative of the queue length, and an estimate of the number of active flows. The proposed mechanism, referred to as DM (diffusion marking), is able to maintain a desired average queue length even under rapid changes in the traffic dynamics with surprisingly short lived queue size transients. DM provides a consistent low link delay without sacrificing throughput and is shown to outperform RED, REM, and AVQ type AQM mechanisms in varying network conditions with a significant improvement in stability.

In the UWB multicarrier receiver, after analog to digital conversion (ADC), the samples of the spectrum of the received signal are used in the digital receiver to estimate the transmitted symbols through a matched filter operation in the discrete frequency domain. The proposed receiver is aimed at the reception of high information rates in a multicarrier signal with very large bandwidth. Thus, the receiver architecture provides a solution to some of the challenging problems found in the implementation of conventional wideband multicarrier receivers based on time-domain ADC, since it parallelizes the A/D conversion, reducing the sampling rate. The receiver is also directly applicable to multicarrier ultra-wideband communication receivers. Additional advantages of the proposed receiver include the possibility of optimally allocating the available number of bits for the A/D conversion across the frequency domain samples, narrowband interference suppression that can be directly carried out in the frequency domain, and inherent robustness to frequency offset which makes it an attractive solution when compared with traditional multicarrier receivers.

Ultrawideband systems employ short low-power pulses. Analog receiver designs can accommodate the required bandwidths, but they come at a cost of reduced flexibility. Digital approaches, on the other hand, provide flexibility in receiver signal processing but are limited by analog-to-digital converter (ADC) resolution and power consumption. In this paper, we consider reduced complexity digital receivers, in which the ADC is limited to a single bit per sample. We study three one-bit ADC schemes: 1) fixed reference; 2) stochastic reference; and 3) sigma-delta modulation (SDM). These are compared for two types of receivers based on: 1) matched filtering; and 2) transmitted reference. Bit-error rate (BER) expressions are developed for these systems and compared to full-resolution implementations with negligible quantization error. The analysis includes the impact of quantization noise, filtering, and oversampling. In particular, for an additive white Gaussian noise channel, we show that the SDM scheme with oversampling can achieve the BER performance of a full-resolution digital receiver.

The paper introduces a new construct of message authentication codes called DBMAC. It can not only provide the message authentication functionality but also localize a few errors in the message. DBMAC uses a conventional MAC in its construction such that it inherits the conventional MACs resistance to forgeries. Furthermore, the division and butterfly structure gives the capability of localizing a few errors. Our construction can be proved to have almost optimal asymptotic tag length. We also extensively analyze the error correction capabilities of our construction for small message length values.

The paper focuses on the queue size estimation problem in random early detection (RED) gateways. Queue size estimation plays a critical role in gateways' packet dropping/marking decisions. Conventional RED gateways use exponentially weighted moving averages (EWMA) to estimate the queue size. These IIR filters require very small weights in order to avoid nonlinear instabilities and accommodate transient congestion. Small weights, however, lead to failure of gateways to track rapid queue size depletion closely and thus causes link under utilization. We use adaptive weighted median filters for queue size estimation and study the corresponding queue dynamics. Simulation results show that the proposed algorithm provides better stability in queue dynamics, greater network power, less global synchronization, and a fairer treatment to bursty traffic than the RED algorithm.

The paper introduces techniques to perform analog-to-digital (A/D) conversion, based on the quantization of the coefficients obtained by the projection of a continuous-time signal over an orthogonal space. This framework for A/D conversion is motivated by the sampling of an input signal in domains which may lead to lower levels of signal distortion and significantly less demanding A/D conversion characteristics. The A/D conversion distortion is reduced by assigning optimal bit rates according to the variance distribution of the coefficients. Moreover, since the quantization of the coefficients is realized at the end of a time window during which the signal is projected, the speed of the quantizers can be much lower than the one needed in conventional time-domain ADCs. In particular, we study ADC in the frequency domain which overcomes some of the difficulties encountered with conventional time-domain A/D conversion of signals with very large bandwidths, such as ultra-wideband (UWB) signals.

In this paper, we show that the optimization needed to solve the least absolute deviations (LAD) regression problem can be viewed as a sequence of maximum likelihood estimates (MLE) of location. The derived algorithm reduces to an iterative procedure where a simple coordinate transformation is applied during each iteration to direct the optimization procedure along edge lines of the cost surface, followed by a MLE estimate of location which is executed by a weighted median operation. Requiring weighted medians only, the new algorithm can be easily modularized for hardware implementation, as opposed to most of the other existing LAD methods which require complicated operations such as matrix entry manipulations. The new algorithm provides a better trade-off solution between convergence speed and implementation complexity compared to existing algorithms.

Weighted median (WM) filtering structures for complex-valued samples have been proposed but none of them allows the use of complex-valued weights. This paper defines complex-valued weighting for median filters with complex-valued input samples. Two different approaches to the handling of weights in the complex domain are presented, both derived from characteristics of complex-valued linear filters, resulting in two definitions of the complex weighted median filter. The LMS optimizations of the proposed filtering schemes are also presented. Simulations are shown illustrating the performance of the new complex WM filter structures compared with previous approaches to the problem and with classical linear filters.

This letter presents a new retransmission timeout (RTO) algorithm based on recursive weighted median (RWM) filters for the transmission control protocol (TCP). The RTO algorithm utilized in current TCP implementations is Jacobson's algorithm, which is based on recursive linear filtering. While linear filters are adequate for estimation in Gaussian signal environments, the round trip time (RTT) signals filtered to determine the RTOs are often impulsive. Thus, Jacobson's algorithm is not effective in many cases. The proposed algorithm employs RWM filters that yield improved performance when operating on RTT signals with heavy tailed statistics. Simulation results show that the proposed method yields significantly tighter RTT bounds than Jacobson's method over Internet traffic with heavy tailed statistics.

Visual cryptography encodes a secret image SI into n shares of random patterns. If the shares are xeroxed onto transparencies, we can visually decode the secret image by superimposing a qualified subset of transparencies, but no secret information can be obtained from the superposition of a forbidden subset. Such a scheme is mathematically secure, however, it produces random patterns which have no visual meaning, raising the suspicion of data encryption. In this paper, to achieve a higher level of security, we propose halftone visual cryptography, where all shares are halftones of grey level images carrying significant visual information. The proposed methods utilize blue-noise dithering principles to construct halftone shares having visually pleasing attributes.

This paper develops mixed signal equalization solutions for gigabit communications in printed circuit boards (PCBs). The PCB channel, composed by vias and interconnects, distorts and produces signal reflections that deteriorate quality of high speed data transmission. Analog signal processing architectures are necessary to combat the ISI effects introduced by the channel since high speed A/D conversion is a very expensive solution. A novel system description and circuit-level architecture that performs mixed-signal feedforward and feedback equalization in the transmit end is introduced. System level simulations show how this combined FF-FB transmit equalizer outperforms the conventional pre-emphasis structures presented in previous works, with a reasonable compromise in circuit area.

A class of robust weighted median (WM) sharpening algorithms is developed in this paper. Unlike traditional linear sharpening methods, weighted median sharpeners are shown to be less sensitive to background random noise or to image artifacts introduced by JPEG and other compression algorithms. These concepts are extended to include data dependent weights under the framework of permutation weighted medians leading to tunable sharpeners that, in essence, are insensitive to noise and compression artifacts. Permutation WM sharpeners are subsequently generalized to smoother/sharpener structures that can sharpen edges and image details while simultaneously filter out background random noise. A statistical analysis of the various algorithms is presented, theoretically validating the characteristics of the proposed sharpening structures. A number of experiments are shown for the sharpening of JPEG compressed images and sharpening of images with background film-grain noise. These algorithms can prove useful in the enhancement of compressed or noisy images posted on the World Wide Web (WWW) as well as in other applications where the underlying images are unavoidably acquired with noise.

A new approach to multichannel image compression is introduced where the intra- and cross-band correlations are jointly exploited in a surprisingly simple yet very effective manner. The key component of the algorithm is a bijection mapping of the original multichannel image into a virtual two-dimensional (2-D) scalar image. By optimally mapping the multichannel image set into a 2-D array and by subsequently applying a scalar image coding algorithm, the spatial correlation and the spectral correlation of the multichannel data set are jointly exploited. Based on the statistical characteristics of the multichannel data, the bijection mapping can be optimized to minimize the distortion introduced by the compression algorithm. The optimization reduces to the maximization of a function of the second-order statistics of the multichannel data. At high compression rates, the new algorithm outperforms traditional compression algorithms whenever the cross-band correlation is high and it yields comparable performance at low compression rates.

A closed-form spectral optimization method for the design of weighted median (WM) filters admitting negative weights is presented. The algorithm is a generalization of Mallows' (1980) theory for nonlinear smoothers that consists of first finding a set of positive weights for a WM filter whose sample selection probabilities are as close as possible to the coefficients of a corresponding finite impulse response (FIR) filter with the desired spectral response. The signs of the weights associated with general WM filtering structures are then coupled with the input samples prior to replication by the weight magnitudes. The spectral characteristics of these WM filters, designed under the proposed method, are shown to be very similar to those of the equivalent linear FIR filters and arbitrary spectral behavior can be achieved. Unlike their FIR filter counterparts, WM filters are robust to impulsive noise, as demonstrated by simulations.

A new approach to digital signatures for imaging, which adapts well to multimedia communications in lossy channels is introduced. Rather than attaching the signature's bit-string as a file-header, it is invisibly etched into the image using a new watermarking algorithm. The watermark is "nonfragile," tolerating small distortions but not malicious tampering aimed at modifying the image's content. In particular, the rank-order relationship in local areas throughout the lowest level of the DWT is exploited to encode the watermark. An edge-based message digest is used. The signature is in the form of binary data and the wavelet decomposition coefficients are modified according to this binary sequence. The signature is also embedded and tested within the SPIHT compression algorithm. The information capacity is studied and the experimental results confirm a logarithm relation between the bit rate and the quantization level, which is similar to the Shannon's capacity theorem. Experiments are performed to examine the signature's transparency and robustness.

This paper introduces approximate image message authentication codes (IMACs) for soft image authentication. The proposed approximate IMAC survives small to moderate image compression and it is capable of detecting and locating tampering. Techniques such as block averaging and smoothing, parallel approximate message authentication code (AMAC) computation, and image histogram enhancement are used in the construction of the approximate IMAC. The performance of the approximate IMAC in three image modification scenarios, namely, JPEG compression, deliberate image tampering, and additive Gaussian noise, is studied and compared. Simulation results are presented.

The output distribution formula for stack filters based on mirrored threshold decomposition is derived. This formula allows one to compute the cumulative distribution function of the output of a stack filter for a given input noise distribution. Mirrored threshold decomposition permits us to analyze the input-output characteristics of the stack filter in the binary domain. The sliding window operation of the stack filter is modeled by a deterministic finite automaton. The output distribution of the filter is obtained by interpreting the automaton as a Markov Chain whose transition probabilities depend on the probabilistic description of the binary input signal.

A generalized recursive weighted median (RWM) filter structure admitting negative weights is introduced. Much like the sample median is analogous to the sample mean, the proposed class of RWM filters is analogous to the class of infinite impulse response (IIR) linear filters. RWM filters provide advantages over linear IIR filters, offering near perfect "stop-band" characteristics and robustness against noise. A novel "recursive decoupling" adaptive optimization algorithm for the design of these RWM filters is also introduced. In the optimization algorithm, the previous outputs used to compute the recursive WM filter output are replaced by previous desired outputs. This structure avoids the feedback inherent in the recursive operation and therefore leads to a much simpler derivation of the gradient in the steepest descent algorithm used to update the filter coefficients.

A new approach to multispectral image compression is introduced where the intra- and cross-band correlations are jointly exploited in a surprisingly simple yet very effective manner. The proposed compression algorithm maps the multispectral image set into a virtual 2-dimensional array and applies a scalar image coding algorithm to the virtual array. Thus, the spatial correlation and the spectral correlation of the multispectral data set are jointly exploited. Based on the statistical characteristics of the multispectral data, the bijection mapping is optimized to minimize the distortion introduced by the compression algorithm. At high compression rates, the new algorithm outperforms traditional compression algorithms whenever the cross-band correlation is high and it yields comparable performance at low compression rates.

In this paper, we introduce two novel techniques for digital color halftoning with green-noise--stochastic dither patterns generated by homogeneously distributing minority pixel clusters. The first technique employs error diffusion with output-dependent feedback where, unlike monochrome image halftoning, an interference term is added such that the overlapping of pixels of different colors can be regulated for increased color control. The second technique uses a green-noise mask, a dither array designed to create green-noise halftone patterns, which has been constructed to also regulate the overlapping of different colored pixels. As is the case with monochrome image halftoning, both techniques are tunable, allowing for large clusters in printers with high dot-gain characteristics, and small clusters in printers with low dot-gain characteristics.

A novel class of robust detectors, the rank order diversity (ROD) detectors, is proposed. The ROD detectors exploit the diversity inherent in any repetition code by sorting the sampled channel output, weighting each of the sorted samples according to their rank, and summing the weighted order statistics to form the test statistic. The ROD detectors subsume the globally optimal detectors for the short-tailed uniform and the normal distributions, as well as the locally optimal detector for the heavy-tailed double-exponential distribution, suggesting a high efficiency of the ROD detectors over a vast range of possible noise statistics. It is shown that for large sample sizes and under mild conditions on the noise statistics, the ROD detector achieves a probability of error less or equal than that of the linear detector with equality only for the normal distribution. The performance of the ROD detectors is illustrated in a DS-CDMA network.

Weighted median filters (smoothers) have been shown to be analogous to normalized FIR linear filters constrained to have only positive weights. In this paper, it is shown that much like the mean is generalized to the rich class of linear FIR fillers, the median can be generalized to a richer class of weighted median (WM) filters admitting positive and negative weights. The generalization follows naturally and is surprisingly simple. In order to analyze and design this class of WM filters, a new threshold decomposition theory admitting real-valued input signals is developed which, in turn, is used to develop fast adaptive algorithms to optimally design the real-valued filter coefficients. The new WM filter formulation leads to significantly more powerful estimators capable of effectively addressing a number of fundamental problems in signal processing which could not adequately be addressed by prior WM filter (smoother) structures.

We introduce the concept of green noise-the mid-frequency component of white noise-and its advantages over blue noise for digital halftoning. Unlike blue noise, which creates the illusion of continuous tone by spreading the minority pixels of a binary dither pattern as homogeneously as possible, green noise forms minority pixel clusters which are themselves distributed as homogeneously as possible. By clustering pixels, green noise patterns are less susceptible to image degradation from printer distortions such as dot-overlap (the overlapping of a printed dot with its nearest neighbors), and by adjusting the average number of pixels per cluster, green noise patterns are tunable to specific printer characteristics. Using both spectral and spatial statistics, are establish models for ideal green noise patterns.

A blind watermarking technique embedding a digital image signature for authentication is developed. The signature algorithm is first implemented in the discrete wavelet transform (DWT) domain and is later coupled within the SPIHT compression algorithm. The capacity of the watermarking method is determined by the upper bound on the attainable information bit rate that can be hidden in the image using two methods: binary engraving and multi-bit engraving.

In this paper, we introduce the concept of green noise-the multifrequency component of white noise-and its advantages over blue noise for digital halftoning. Unlike blue-noise dither patterns, which are composed exclusively of isolated pixels, green-noise dither patterns are composed of pixel-clusters making them less susceptible to image degradation from nonideal printing artifacts such as dot-gain. Although they are not the only techniques which generate clustered halftones, error-diffusion with output-dependent feedback and variations based on filter weight perturbation are shown to be good generators of green noise, thereby allowing for tunable coarseness. Using statistics developed for blue noise, we closely examine the spectral content of resulting dither patterns. We introduce two spatial-domain statistics for analyzing the spatial arrangement of pixels in aperiodic dither patterns, because green noise patterns may be anisotropic, and therefore spectral statistics based on radial averages may be inappropriate for the study of these patterns.

The rank ordering of samples is widely used in robust statistics and robust signal processing. Advances in these areas have focused on utilizing joint time-rank (TR) information. The TR information utilized to date is that resulting from a binary, or crisp, relation between the marginal time and rank ordering of samples. This crisp relation, while powerful, contains no information on sample values or spread. This paper generalizes the TR relation through fuzzy set theory. This generalization includes information on sample spread and leads to the concepts of fuzzy TR relations, fuzzy time and rank ordered samples, and fuzzy time and rank indices. These concepts are developed and analyzed through the derivation of fundamental properties. It is shown that the fuzzy TR relations, samples, and indices contain their crisp (standard) counterparts as special cases. These fuzzy generalizations constitute powerful tools that can be exploited in the design of signal processing algorithms.

We introduce a novel, data-adaptive, and robust filtering framework: affine order statistic filters. Affine order statistics relate classical order statistics to observations in their natural order and thus inherently yield a meaningful data representation. Affine order statistic filters exploit this notion to adaptively process nonstationary signals. Affine order statistic filters overcome many of the limitations associated with traditional order statistic filters, in particular: filters in this class are parsimonious in the number of filter coefficients, they are statistically efficient in a wide range of signal statistics, and they admit real-valued filter weights leading to a wide-range of filtering characteristics. The class of affine order statistic filters contains two families: the weighted order statistic (WOS) affine fitter class whose structure can adapt, according to the observed data, from an FIR linear filter to a WOS filter, and the FIR affine filter class whose structure can adapt from an L-filter to an FIR-filter. We introduce the median affine filter and the center affine filter as representatives of each class, and show their performance in two applications where the signals are nonstationary in nature.

In this paper we introduce a general framework for edge preserving filters, derived from the powerful class of M-estimators. First, we show that under very general assumptions, any location estimator generates an edge preserving filter if we approximate the estimate by one of the input samples. Based on this premise, we propose the family of S-estimators or S-filters, as a selection-type class of filters arising from a computationally tractable "selectification" of location M-estimators. S-filters inherit the richness of the theory underlying the M-estimators framework, providing a very flexible family of robust estimators with edge preservation capabilities. Several properties of S-filters are studied. Sufficient and necessary conditions are given for an S-filter to present edge enhancing capabilities, and several novel filters within this framework are introduced and illustrated. Data, figures and source code utilized in this paper are available at http://www.ee.udel.edu/signals/robust/.

Stochastic gradient-based adaptive algorithms are developed for the optimization of weighted myriad filters, a class of nonlinear filters, motivated by the properties of /spl alpha/-stable distributions, that have been proposed for robust non-Gaussian signal processing in impulsive noise environments. An implicit formulation of the filter output is used to derive an expression for the gradient of the mean absolute error (MAE) cost function, leading to necessary conditions for the optimal filter weights. An adaptive steepest-descent algorithm is then derived to optimize the filter weights. This is modified to yield an algorithm with a very simple weight update, computationally comparable to the update in the classical LMS algorithm. Simulations demonstrate the robust performance of these algorithms.

We introduce a new multiresolution watermarking method for digital images. The method is based on the discrete wavelet transform (DWT). Pseudo-random codes are added to the large coefficients at the high and middle frequency bands of the DWT of an image. It is shown that this method is more robust to often proposed methods to some common image distortions, such as the wavelet transform based image compression, and image halftoning. Moreover, the method is hierarchical. The computation load needed to detect the watermark depends on the noise level in an image.

With the emergence of advanced display media as well as digital video coding and compression schemes came a variety of new video formats including program content dependent formats, as proposed by the Grand Alliance for their high definition television (HDTV) standard. Digital video down-conversion is a low complexity quality reduction task, whereas the more complex video up-conversion incorporates a tradeoff between computational cost and perceptual quality. Motion-compensated conversion algorithms have the potential for good results, but go in hand with a computational complexity disadvantage, whereas motion-adaptive interpolation methods constitute a compromise between the extremes. This paper presents a general motion-adaptive format conversion approach based on a multiresolution decomposition and nonlinear subband interpolation filtering. The class of Ll permutation filters feature a flexible, input-signal dependent behavior by exploiting the order statistics of an input signal. In this paper, such an approach is utilized for interpolation purposes, applicable to any arbitrary format conversion problem. A successful application of Ll filter based interpolators in combination with a hierarchical multiresolution decomposition as a motion-adaptive format conversion method is presented. As an evaluation of performance, two format conversion case studies are presented, namely deinterlacing for progressive display media and frame-rate up-conversion for the reduction of temporal artifacts.

We introduce a robust and nonlinear filtering framework: weighted myriad filtering. Much like the Gaussian assumption has motivated the development of linear filtering theory, the formulation of myriad filters is motivated by the statistical properties of /spl alpha/-stable processes. Weighted myriad filters have a solid theoretical basis, are inherently more powerful than weighted median filters, and are very general subsuming traditional linear FIR filters. The foundation of the proposed filtering algorithms lies in the definition of the sample myriad as the location estimate for a class of /spl alpha/-stable distributions. In turn, the myriad has been discovered as the location parameter estimated by the sample myriad. This paper addresses some theoretical properties of myriad filters. The superior performance of myriad filters in impulsive environments is illustrated in the problem of robust synchronization by means of a "myriad phase lock loop".

We report our results concerning the study of multivariate functions of threshold-decomposed signals. In particular we show that multilinear tensor forms of the decomposed signal yield a class of filters that we propose to call piecewise Volterra filters (PWV). A filter can be viewed as a transformation of /spl Rscr//sup N//spl rarr//spl Rscr/, where N is the number of filter taps. PWV filters partition /spl Rscr//sup N/ using a hyper-rectangular lattice, and assign a Volterra filter to each of the partition regions. At the partition boundaries continuity between the multivariate polynomials is preserved resulting in class /spl Cscr//sup 0/ piecewise polynomials. PWV filters constitute an efficient alternative for describing some systems rich in hard nonlinear structures, especially since parameter estimation remains a linear problem for PWVs.

Donoho and Johnstone (1992) first introduced wavelet shrinkage as a denoising technique for signals embedded in Gaussian noise, but due to the linearity of wavelet decomposition, wavelet shrinkage is ineffective in non-Gaussian noise which exhibits outliers. We evaluate two schemes which have been developed to extend the denoising capabilities of wavelet shrinkage to signals corrupted by non-Gaussian noise. The first scheme introduced by Bruce et al. (see Proceedings SPIE Conference, 1994) smoother-cleaner wavelets integrates median filters into the wavelet decomposition. The second scheme, introduced by the authors, replaces the linear filters of wavelet decomposition with order statistic based Chameleon filters. We also show that a straight forward extension of these schemes to images does not offer the same effectiveness in denoising as they do with one dimensional signals.

Filter banks play a major role in multirate signal processing where these have been successfully used in a variety of applications. In the past, filter banks have been developed within the framework of linear filters. It is well known, however, that linear filters may have less than satisfactory performance whenever the underlying processes are non-Gaussian. We introduce the nonlinear class of order statistic (OS) filter banks that exploit the spectral characteristics of the input signal as well as its rank-ordering structure. The attained subband signals provide frequency and rank information in a localized time interval. OS filter banks can lead to significant gains over linear filter banks, particularly when the input signals contain abrupt changes and details, as is common with image and video signals. OS filter banks are formed using traditional linear filter banks as fundamental building blocks. It is shown that OS filter banks subsume linear filter banks and that the latter are obtained by simple linear transformations of the former. To illustrate the properties of OS filter banks, we develop simulations showing that the learning characteristics of the LMS algorithm, which are used to optimize the weight taps of OS filters, can be significantly improved by performing the adaptation in the OS subband domain.

Vector order statistic based filters designed to exploit the correlation between the channels of a multichannel signal offer improved performance over purely marginal processing. In this paper, the class of permutation filters are extended to handle multichannel signals. Permutation filters are well suited for image processing; they are robust, able to preserve details, and edges in image and video signals, and can also model complicated non-linear systems accurately. Multichannel permutation filters are based on the permutation of a set of sequential observations from a multidimensional process. There exists no unique method for the ranking of vectors, so we evaluate two ranking formulations that preserve characteristics useful in constructing estimators. Simulation results for a video restoration problem are presented.

We introduce and analyze a new class of nonlinear filters called permutation weighted order statistic (PWOS) filters. These filters extend the concept of weighted order statistic (WOS) filters, in which filter weights associated with the input samples are used to replicate the corresponding samples, and an order statistic is chosen as the filter output. PWOS filters replicate each input sample according to weights determined by the temporal-order and rank-order of samples within a window. Hence, PWOS filters are in essence time-varying WOS filters. By varying the amount of temporal-rank order information used in selecting the output for a given observation window size, we obtain a wide range of filters that are shown to comprise a complete lattice structure. At the simplest level in the lattice, PWOS filters reduce to the well-known WOS filter, but for higher levels in the lattice, the obtained selection filters can model complex nonlinear systems and signal distortions. It is shown that PWOS filters are realizable by a N! piecewise linear threshold logic gate where the coefficients within each partition can be easily optimized using stack filter theory. Simulations are included to show the advantages of PWOS filters for the processing of image and video signals.

The problem of reconstructing a continuous-tone image given its ordered dithered halftone or its error-diffused halftone image is considered. We develop a modular class of nonlinear filters that can reconstruct the continuous-tone information preserving image details and edges that provide important visual cues. The proposed nonlinear reconstruction algorithms, denoted as binary permutation filters, are based on the space and rank orderings of the halftone samples provided by the multiset permutation of the "on" pixels in a halftone observation window. For a given window size, we obtain a wide range of filters by varying the amount of space-rank ordering information utilized in the estimate. For image reconstructions from ordered dithered halftones, we develop periodically space-varying filters that can account for the periodical nature of the underlying screening process. A class of suboptimal but simpler space-invariant reconstruction filters are also proposed and tested. Constrained LMS type algorithms are employed for the design of reconstruction filters that minimize the reconstruction mean squared error. We present simulations showing that binary permutation filters are modular, robust to image source characteristics, and that they produce high visual quality image reconstruction.

Filter banks play a major role in multirate signal processing where these have been succesfully used in a variety of applications. In the past, filter banks have been developed within the framework of linear filters. In this paper, we introduce filter banks which exploit the input signal spectral characteristics as well as the signal's rank-ordering structure. Order-Statistic filter basks can lead to significant gains over linear filter banks, particularly when the input signals contain abrupt changes and details, as is common with image and video signals. It is shown that OS filter banks subsume linear filter banks and that the later are obtained by simple linear transformations of the former. The methods derived here can be utilized with uniform or non-nonuniform subband filter banks.>

The problem of reconstructing a continuous-tone image given its ordered dithered halftone image is considered. We utilize a modular class of non-linear filters, denoted as binary permutation filters, which can reconstruct the continuous-tone information as well as image details which provide important visual cues. Binary permutation filters are based on the space-rank ordering of the halftone samples which is provided by the multiset permutation of the "on" pixels in a halftone observation window. By varying the space-rank order information utilized in the estimate, for a given window size, we obtain a wide range of filters. We present simulations showing that binary permutation filters are modular, robust to image source characteristics, and that their results produce high visual quality image reconstruction.>

The extension of ranking a set of elements in R to ranking a set of vectors in a p'th dimensional space R/sup p/ is considered. In the approach presented here vector ranking reduces to ordering vectors according to a sorted list of vector distances. A statistical analysis of this vector ranking is presented, and these vector ranking concepts are then used to develop ranked-order type estimators for multivariate image fields. A class of vector filters is developed, which are efficient smoothers in additive noise and can be designed to have detail-preserving characteristics. A statistical analysis is developed for the class of filters and a number of simulations were performed in order to quantitatively evaluate their performance. These simulations involve the estimation of both stationary multivariate random signals and color images in additive noise.>

The authors discuss detail-preserving, ranked-order based filtering algorithms. These filters fall, roughly, into one of two categories: adaptive and non-adaptive. The main advantage of non-adaptive filters is that neither a-priori information of the image is required, nor does one need to compute local statistics inside the filters window. The authors consider non-adaptive, structure preserving filters only. In particular, they analyze the class of multilevel median filters, and compare their efficiency with that of other detail-preserving filters including multilevel FIR-median hybrid and morphological filters. For completeness, they also include results for the square median filter.>

A means of improving the ordered dither halftoning algorithm by the use of unconventional screen periodicities is discussed. It is shown that altering the periodicity matrix frequently shifts the location of the halftone spectral orders into a region of the Omega plane to which the human visual system is less sensitive. Consequently, optimal patterns for these periodicities exhibit a lower degree of false contours and textures and outperform traditional dither patterns. A few representative periodic tessellations that produce typical results are examined. It is also shown that the concepts introduced can be applied to the angled screens created by Holladay's technique.>

Vector probability measure functions (density function) for recursively median filtered signals are found when the underlying input binary sequences are either independent identically distributed (i.i.d.) or Markov chains. The results are parametric in the window size of the filter and in the probability distribution of the input sequence. Using statistical threshold decomposition, the same results are found for discrete alphabet random sequences that are either i.i.d. or Markov chains. Some examples illustrating the efficacy of the recursive median filter relative to the nonrecursive implementation are presented. In particular, the breakdown probabilities are tabulated for both recursive and nonrecursive median filters.>

The statistical analysis of recursive nonlinear filters is generally difficult. The analysis of recursive median filters has been limited to the trivial cases of signals with a small number of quantization levels and to small window sizes. A block state description of recursively filtered signals is developed, and by applying this description to threshold decomposition, closed-form expressions for the statistics of recursive median filters are obtained. In this case, the number of quantization levels and the window size do not increase the analysis complexity since the output statistics depend on the distribution of a single-threshold filtered binary signal. The statistical decomposition is also developed for nonrecursive median filter operations yielding a connection from classical order statistics to the threshold decomposition approach. Finally, some statistical properties are derived for recursively median-filtered signals.

Median filtering is a nonlinear technique for smoothing signals. In this paper we find the output distribution of recursively median filtered two dimensional signals with additive impulsive noise. We study the edge jitter effect that recursive median filtering introduces. Finally some examples are included illustrating these results.

In this paper we source encode the truncated block used in block truncation coding. It is shown that the truncated block is well approximated by wide-sense Markoff statistics; a signal having these characteristics has a high probability of belonging to the root signal set of median filters. Because the root signal space is much smaller than the binary space, it takes fewer bits to specify the truncated block in the root signal space, obtaining in this manner rate compression. Using two-dimensional filtering we can reduce the standard BTC rate of 1.63 bits/pel to 1.31 bits/pel. Using one-dimensional filtering along with a trellis encoder, rates close to 1.1 bits/pel are obtained with this fixed-length coding method.