A new Bayesian model for image segmentation based on a Gaussian mixture model is proposed. The model structure allows the automatic determination of the number of segments while ensuring spatial smoothness of the final output. This is achieved by defining two separate mixture weight sets: the first set of weights is spatially variant and incorporates an MRF edge-preserving smoothing prior; the second set of weights is governed by a Dirichlet prior in order to prune unnecessary mixture components. The model is trained using variational inference and the Majorization-Minimization (MM) algorithm, resulting in closed-form parameter updates. The algorithm was successfully evaluated in terms of various segmentation indices using the Berkeley image data base.

Super-resolution (SR) is the term used to define the process of estimating a high-resolution (HR) image or a set of HR images from a set of low-resolution (LR) observations. In this paper we propose a class of SR algorithms based on the maximum a posteriori (MAP) framework. These algorithms utilize a new multichannel image prior model, along with the state-of-the-art single channel image prior and observation models. A hierarchical (two-level) Gaussian nonstationary version of the multichannel prior is also defined and utilized within the same framework. Numerical experiments comparing the proposed algorithms among themselves and with other algorithms in the literature, demonstrate the advantages of the adopted multichannel approach.

In this paper, a new image prior is introduced and used in image restoration. This prior is based on products of spatially weighted total variations (TV). These spatial weights provide this prior with the flexibility to better capture local image features than previous TV based priors. Bayesian inference is used for image restoration with this prior via the variational approximation. The proposed restoration algorithm is fully automatic in the sense that all necessary parameters are estimated from the data and is faster than previous similar algorithms. Numerical experiments are shown which demonstrate that image restoration based on this prior compares favorably with previous state-of-the-art restoration algorithms.

A new Bayesian model is proposed for image segmentation based upon Gaussian mixture models (GMM) with spatial smoothness constraints. This model exploits the Dirichlet compound multinomial (DCM) probability density to model the mixing proportions (i.e., the probabilities of class labels) and a Gauss-Markov random field (MRF) on the Dirichlet parameters to impose smoothness. The main advantages of this model are two. First, it explicitly models the mixing proportions as probability vectors and simultaneously imposes spatial smoothness. Second, it results in closed form parameter updates using a maximum a posteriori (MAP) expectation-maximization (EM) algorithm. Previous efforts on this problem used models that did not model the mixing proportions explicitly as probability vectors or could not be solved exactly requiring either time consuming Markov Chain Monte Carlo (MCMC) or inexact variational approximation methods. Numerical experiments are presented that demonstrate the superiority of the proposed model for image segmentation compared to other GMM-based approaches. The model is also successfully compared to state of the art image segmentation methods in clustering both natural images and images degraded by noise.

Super-resolution (SR) algorithms for compressed video aim at recovering high-frequency information and estimating a high-resolution (HR) image or a set of HR images from a sequence of low-resolution (LR) video frames. In this paper we present a novel SR algorithm for compressed video based on the maximum a posteriori (MAP) framework. We utilize a new multichannel image prior model, along with the state-of-the art image prior and observation models. Moreover, relationship between model parameters and the decoded bitstream are established. Numerical experiments demonstrate the improved performance of the proposed method compared to existing algorithms for different compression ratios.

We propose a new approach for the restoration of polarimetric Stokes images, capable of simultaneously segmenting and restoring the images. In order to easily handle the admissibility constraints inherent to Stokes images, a proper transformation of the images is introduced. This transformation exploits the correspondence between any Stokes vector and the covariance matrix of the two components of the electric vector of the light wave. A Bayesian model based on a mixture of Gaussian kernels is used for the transformed images. Inference is achieved using the EM framework. To quantify the performances of this approach, the algorithm is tested with both synthetic and real data. We note that the pixels of the restored Stokes images issued from our approach are always physically admissible which is not the case for the nai¿ve pseudo-inverse approach.

A new relevance feedback (RF) approach for content-based image retrieval is presented. This approach uses Gaussian mixture (GM) models of the image features and a query that is updated in a probabilistic manner. This update reflects the preferences of the user and is based on the models of both the positive and negative feedback images. The retrieval is based on a recently proposed distance measure between probability density functions, which can be computed in closed form for GM models. The proposed approach takes advantage of the form of this distance measure and updates it very efficiently based on the models of the user-specified relevant and irrelevant images. It is also shown that this RF framework is fairly general and can be applied in case other image models or distance measures are used instead of those proposed in this work. Finally, comparative numerical experiments are provided, which that demonstrate the merits of the proposed RF methodology and the use of the distance measure, and also the advantages of using GMs for image modelling.

In this paper, we present a new Bayesian model for the blind image deconvolution (BID) problem. The main novelty of this model is the use of a sparse kernel-based model for the point spread function (PSF) that allows estimation of both PSF shape and support. In the herein proposed approach, a robust model of the BID errors and an image prior that preserves edges of the reconstructed image are also used. Sparseness, robustness, and preservation of edges are achieved by using priors that are based on the Student's-t probability density function (PDF). This pdf, in addition to having heavy tails, is closely related to the Gaussian and, thus, yields tractable inference algorithms. The approximate variational inference methodology is used to solve the corresponding Bayesian model. Numerical experiments are presented that compare this BID methodology to previous ones using both simulated and real data.

Video indexing requires the efficient segmentation of video into scenes. The video is first segmented into shots and a set of key-frames is extracted for each shot. Typical scene detection algorithms incorporate time distance in a shot similarity metric. In the method we propose, to overcome the difficulty of having prior knowledge of the scene duration, the shots are clustered into groups based only on their visual similarity and a label is assigned to each shot according to the group that it belongs to. Then, a sequence alignment algorithm is applied to detect when the pattern of shot labels changes, providing the final scene segmentation result. In this way shot similarity is computed based only on visual features, while ordering of shots is taken into account during sequence alignment. To cluster the shots into groups we propose an improved spectral clustering method that both estimates the number of clusters and employs the fast global k-means algorithm in the clustering stage after the eigenvector computation of the similarity matrix. The same spectral clustering method is applied to extract the key-frames of each shot and numerical experiments indicate that the content of each shot is efficiently summarized using the method we propose herein. Experiments on TV-series and movies also indicate that the proposed scene detection method accurately detects most of the scene boundaries while preserving a good tradeoff between recall and precision.

Sparse kernel methods are very efficient in solving regression and classification problems. The sparsity and performance of these methods depend on selecting an appropriate kernel function, which is typically achieved using a cross-validation procedure. In this paper, we propose an incremental method for supervised learning, which is similar to the relevance vector machine (RVM) but also learns the parameters of the kernels during model training. Specifically, we learn different parameter values for each kernel, resulting in a very flexible model. In order to avoid overfitting, we use a sparsity enforcing prior that controls the effective number of parameters of the model. We present experimental results on artificial data to demonstrate the advantages of the proposed method and we provide a comparison with the typical RVM on several commonly used regression and classification data sets.

A new hierarchical Bayesian model is proposed for image segmentation based on Gaussian mixture models (GMM) with a prior enforcing spatial smoothness. According to this prior, the local differences of the contextual mixing proportions (i.e. the probabilities of class labels) are Studentpsilas t-distributed. The generative properties of the Student's t-pdf allow this prior to impose smoothness and simultaneously model the edges between the segments of the image. A maximum a posteriori (MAP) expectation-maximization (EM) based algorithm is used for Bayesian inference. An important feature of this algorithm is that all the parameters are automatically estimated from the data in closed form. Numerical experiments are presented that demonstrate the superiority of the proposed model for image segmentation as compared to standard GMM-based approaches and to GMM segmentation techniques with ldquostandardrdquo spatial smoothness constraints.

In this paper a relevance feedback (RF) approach for content based image retrieval (CBIR) is described and evaluated. The approach uses Gaussian mixture (GM) models of the image features and a query that is updated in a probabilistic manner. This update reflects the preferences of the user and is based on the models of both positive and negative feedback images. Retrieval is based on a recently proposed distance measure between probability density functions (pdfs), which can be computed in closed form for GM models. The proposed approach takes advantage of the form of this distance measure and updates it very efficiently based on the models of the user specified relevant and irrelevant images. For evaluation purposes, comparative experimental results are presented that demonstrate the merits of the proposed methodology.

In this paper, we propose a new family of watermark detectors for additive watermarks in digital images. These detectors are based on a recently proposed hierarchical, two-level image model, which was found to be beneficial for image recovery problems. The top level of this model is defined to exploit the spatially varying local statistics of the image, while the bottom level is used to characterize the image variations along two principal directions. Based on this model, we derive a class of detectors for the additive watermark detection problem, which include a generalized likelihood ratio, Bayesian, and Rao test detectors. We also propose methods to estimate the necessary parameters for these detectors. Our numerical experiments demonstrate that these new detectors can lead to superior performance to several state-of-the-art detectors.

Image priors based on products have been recognized to offer many advantages because they allow simultaneous enforcement of multiple constraints. However, they are inconvenient for Bayesian inference because it is hard to find their normalization constant in closed form. In this paper, a new Bayesian algorithm is proposed for the image restoration problem that bypasses this difficulty. An image prior is defined by imposing Student-t densities on the outputs of local convolutional filters. A variational methodology, with a constrained expectation step, is used to infer the restored image. Numerical experiments are shown that compare this methodology to previous ones and demonstrate its advantages.

In this paper we propose a new family of watermark detectors for additive watermarks in digital images. These detectors are based on a recently proposed two-level, hierarchical image model, which was found to be beneficial for image recovery problems. The top level of this model is defined to exploit the spatially-varying local statistics of the image, while the bottom level is used to characterize the image variations along two principal directions. Based on this model we derive a class of detectors for the additive watermark detection problem, including the generalized likelihood ratio test (GLRT) and Rao detectors.

Gaussian mixture models have been widely used in image segmentation. However, such models are sensitive to outliers. In this paper, we consider a robust model for image segmentation based on mixtures of Student'st-distributions which have heavier tails than Gaussian and thus are not sensitive to outliers. Thet-distribution is one of the few heavy tailed probability density functions (pdf) closely related to the Gaussian, that gives tractable maximum likelihood inference via the Expectation-Maximization (EM) algorithm. Numerical experiments that demonstrate the properties of the proposed model for image segmentation are presented.

In this paper we present a new Bayesian model for the blind image deconvolution (BID) problem. The main novelties of this model are three. The first one is the use of a sparse kernel-based model for the point spread function (PSF) that allows estimation of both PSF shape and support. The second one is a robust distribution of the BID model errors and the third novelty is an image prior that preserves edges of the reconstructed image. Sparseness, robustness and preservation of edges is achieved by using priors that are based on the Student-t probability density function (pdf). The Variational methodology is used to solve the corresponding Bayesian model. Numerical experiments are presented that demonstrate the advantages of this model as compared to previous Gaussian based ones.

In this paper we present a new approach for curve clustering designed for analysis of spatiotemporal data. Such kind of data contains both spatial and temporal patterns that we desire to capture. The proposed methodology is based on regression and Gaussian mixture modeling and the novelty of the herein work is the incorporation of spatial smoothness constraints in the form of a prior for the data labels. This enables the proposed model to take into account the underlying property of spatiotemporal data that spatially adjacent data points most likely should belong to the same cluster. A maximum a posteriori Expectation Maximization (MAP-EM) algorithm is used for learning this model. We present numerical experiments with simulated data where the ground truth is known in order to assess the value of the introduced smoothness constraint, and also with real cardiac perfusion MRI data. The results are very promising and demonstrate the value of the proposed constraint for analysis of such data .

Video indexing requires the efficient segmentation of the video into scenes. In the method we propose, the video is first segmented into shots and key-frames are extracted using the global k-means clustering algorithm that represent each shot. Then an improved spectral clustering method is applied to cluster the shots into groups based on visual similarity and a label is assigned to each shot according to the group that it belongs to. Next, a method for segmenting the sequence of shot labels is applied, providing the final scene segmentation result. Numerical experiments indicate that the method we propose correctly detects most of the scene boundaries while preserving a good trade off between recall and precision.

In this paper we present new detectors for additive watermarks when the power of the watermark is unknown. These detectors are based on modeling the image using student-t statistics. As a result, due to the generative properties of the student-t density function, such models are spatially adaptive and the Expectation-Maximization algorithm can be used to obtain maximum likelihood estimates of their parameters. Using these image models detectors based on the generalized likelihood ratio and Rao tests are derived for this problem. Numerical experiments are presented that demonstrate the properties of these detectors and compared them with previously proposed detectors.

In this paper, we propose a maximum a posteriori ramework for the super-resolution problem, i.e., reconstructing high-resolution images from shifted, rotated, low-resolution degraded observations. The main contributions of this work are two; first, the use of a new locally adaptive edge preserving prior for the super-resolution problem. Second an efficient two-step reconstruction methodology that includes first an initial registration using only the low-resolution degraded observations. This is followed by a fast iterative algorithm implemented in the discrete Fourier transform domain in which the restoration, interpolation and the registration subtasks of this problem are preformed simultaneously. We present examples with both synthetic and real data that demonstrate the advantages of the proposed framework.

We propose a new approach for image segmentation based on a hierarchical and spatially variant mixture model. According to this model, the pixel labels are random variables and a smoothness prior is imposed on them. The main novelty of this work is a new family of smoothness priors for the label probabilities in spatially variant mixture models. These Gauss-Markov random field-based priors allow all their parameters to be estimated in closed form via the maximum a posteriori (MAP) estimation using the expectation-maximization methodology. Thus, it is possible to introduce priors with multiple parameters that adapt to different aspects of the data. Numerical experiments are presented where the proposed MAP algorithms were tested in various image segmentation scenarios. These experiments demonstrate that the proposed segmentation scheme compares favorably to both standard and previous spatially constrained mixture model-based segmentation.

We propose an approach to analyzing functional neuroimages in which 1) regions of neuronal activation are described by a superposition of spatial kernel functions, the parameters of which are estimated from the data and 2) the presence of activation is detected by means of a generalized likelihood ratio test (GLRT). Kernel methods have become a staple of modern machine learning. Herein, we show that these techniques show promise for neuroimage analysis. In an on-off design, we model the spatial activation pattern as a sum of an unknown number of kernel functions of unknown location, amplitude, and/or size. We employ two Bayesian methods of estimating the kernel functions. The first is a maximum a posteriori (MAP) estimation method based on a Reversible-Jump Markov-chain Monte-Carlo (RJMCMC) algorithm that searches for both the appropriate model complexity and parameter values. The second is a relevance vector machine (RVM), a kernel machine that is known to be effective in controlling model complexity (and thus discouraging overfitting). In each method, after estimating the activation pattern, we test for local activation using a GLRT. We evaluate the results using receiver operating characteristic (ROC) curves for simulated neuroimaging data and example results for real fMRI data. We find that, while RVM and RJMCMC both produce good results, RVM requires far less computation time, and thus appears to be the more promising of the two approaches.

In this paper, we propose a class of image restoration algorithms based on the Bayesian approach and a new hierarchical spatially adaptive image prior. The proposed prior has the following two desirable features. First, it models the local image discontinuities in different directions with a model which is continuous valued. Thus, it preserves edges and generalizes the on/off (binary) line process idea used in previous image priors within the context of Markov random fields (MRFs). Second, it is Gaussian in nature and provides estimates that are easy to compute. Using this new hierarchical prior, two restoration algorithms are derived. The first is based on the maximum a posteriori principle and the second on the Bayesian methodology. Numerical experiments are presented that compare the proposed algorithms among themselves and with previous stationary and non stationary MRF-based with line process algorithms. These experiments demonstrate the advantages of the proposed prior.

Using a stochastic framework, we propose two algorithms for the problem of obtaining a single high-resolution image from multiple noisy, blurred, and undersampled images. The first is based on a Bayesian formulation that is implemented via the expectation maximization algorithm. The second is based on a maximum a posteriori formulation. In both of our formulations, the registration, noise, and image statistics are treated as unknown parameters. These unknown parameters and the high-resolution image are estimated jointly based on the available observations. We present an efficient implementation of these algorithms in the frequency domain that allows their application to large images. Simulations are presented that test and compare the proposed algorithms.

In this paper the problem of detecting and localizing an object embedded in a background image from photon-limited observations is addressed. A new algorithm based on the generalized likelihood ratio test (GLRT) algorithm is formulated and compared to traditional detectors for images in photon-limited noise. We used Monte-Carlo estimation of the localization-receiver-operating characteristics (LROC) curve to evaluate the performance of the proposed algorithm quantitatively and compare it with existing methods. Our experimental results demonstrate that the proposed GLRT approach significantly outperforms traditional photon-limited detectors.

In this paper we propose a new hierarchical non stationary image prior for image restoration. This prior captures the directional edges using a continuous model and regularizes accordingly the restored images. In addition, the corresponding generative graphical model does not contain cycles, thus learning this model is easy and fast. Based on this prior image model, a maximum a posteriori (MAP) estimation algorithm is derived. Numerical experiments are provided that demonstrate the advantages of the proposed non stationary model as compared with algorithms that use stationary models.

We propose a new solution to the problem of obtaining a single high-resolution image from multiple blurred, noisy, and undersampled images. Our estimator, derived using the Bayesian stochastic framework, is novel in that it employs a new hierarchical non-stationary image prior. This prior adapts the restoration of the super-resolved image to the local spatial statistics of the image. Numerical experiments demonstrate the effectiveness of the proposed approach.

In this paper, we propose a new methodology for analysis of microarray images. First, a new gridding algorithm is proposed for determining the individual spots and their borders. Then, a Gaussian mixture model (GMM) approach is presented for the analysis of the individual spot images. The main advantages of the proposed methodology are modeling flexibility and adaptability to the data, which are well-known strengths of GMM. The maximum likelihood and maximum a posteriori approaches are used to estimate the GMM parameters via the expectation maximization algorithm. The proposed approach has the ability to detect and compensate for artifacts that might occur in microarray images. This is accomplished by a model-based criterion that selects the number of the mixture components. We present numerical experiments with artificial and real data where we compare the proposed approach with previous ones and existing software tools for microarray image analysis and demonstrate its advantages.

Gaussian mixture models (GMMs) constitute a well-known type of probabilistic neural networks. One of their many successful applications is in image segmentation, where spatially constrained mixture models have been trained using the expectation-maximization (EM) framework. In this letter, we elaborate on this method and propose a new methodology for the M-step of the EM algorithm that is based on a novel constrained optimization formulation. Numerical experiments using simulated images illustrate the superior performance of our method in terms of the attained maximum value of the objective function and segmentation accuracy compared to previous implementations of this approach.

In this paper, we describe an approach to content-based retrieval of medical images from a database, and provide a preliminary demonstration of our approach as applied to retrieval of digital mammograms. Content-based image retrieval (CBIR) refers to the retrieval of images from a database using information derived from the images themselves, rather than solely from accompanying text indices. In the medical-imaging context, the ultimate aim of CBIR is to provide radiologists with a diagnostic aid in the form of a display of relevant past cases, along with proven pathology and other suitable information. CBIR may also be useful as a training tool for medical students and residents. The goal of information retrieval is to recall from a database information that is relevant to the user's query. The most challenging aspect of CBIR is the definition of relevance (similarity), which is used to guide the retrieval machine. In this paper, we pursue a new approach, in which similarity is learned from training examples provided by human observers. Specifically, we explore the use of neural networks and support vector machines to predict the user's notion of similarity. Within this framework we propose using a hierarchal learning approach, which consists of a cascade of a binary classifier and a regression module to optimize retrieval effectiveness and efficiency. We also explore how to incorporate online human interaction to achieve relevance feedback in this learning framework. Our experiments are based on a database consisting of 76 mammograms, all of which contain clustered microcalcifications (MCs). Our goal is to retrieve mammogram images containing similar MC clusters to that in a query. The performance of the retrieval system is evaluated using precision-recall curves computed using a cross-validation procedure. Our experimental results demonstrate that: 1) the learning framework can accurately predict the perceptual similarity reported by human observers, thereby serving as a basis for CBIR; 2) the learning-based framework can significantly outperform a simple distance-based similarity metric; 3) the use of the hierarchical two-stage network can improve retrieval performance; and 4) relevance feedback can be effectively incorporated into this learning framework to achieve improvement in retrieval precision based on online interaction with users; and 5) the retrieved images by the network can have predicting value for the disease condition of the query.

Image processing for analysis of microarray images is an important and challenging problem because imperfections and fabrication artifacts often impair our ability to measure accurately the quantities of interest in these images. In this paper we propose a microarray image analysis framework that provides a new method that automatically addresses each spot area in the image. Then, a new unsupervised clustering method is used which is based on a Gaussian mixture model (GMM) and the minimum description length (MDL) criterion, that allows the automatic spot area segmentation and the image artifacts isolation and correction to obtain more accurate spot quantitative values. Experimental results demonstrates the advantages of the proposed scheme in efficiently analysing microarrays.

In this work we explore the use of a content-adaptive mesh model (CAMM) in the classical problem of image restoration. In the proposed framework, we first model the image to be restored by an efficient mesh representation. A CAMM can be viewed as a form of image representation using nonuniform samples, of which the mesh nodes (i.e., image samples) are adaptively placed according to the local content of the image. The image is then restored through estimating the model parameters (i.e., mesh nodal values) from the data. A CAMM provides a natural spatially-adaptive regularization mechanism for image restoration in that the interpolation basis functions in a CAMM have their spatial support varying with the local image content. We present some exploratory results to demonstrate the proposed approach.

In this paper, a watermark pattern design approach is proposed to combat the general geometric attacks to watermarking systems. Geometric attacks pose a major threat to most existing watermarking systems by destroying the synchronization between the watermark patterns and the watermarked images. We propose to shape the watermark patterns so that the output of the correlation-type demodulator is in the shape of a specified function. Such a watermark pattern shaping can be used directly to combat moderate geometric attack, or used with other watermark schemes to improve decoding performance. A design example of the shaping filter is presented. Experiments show that the proposed watermarking scheme can survive survive (1999) bending attack to a wide range.

In this work we explore a new technique for relevance feedback in a learning-based framework for retrieval of relevant mammogram images from a database, for purposes of aiding diagnoses. Our goal is to adapt online the learning procedure in accordance with user responses without the need to repeat the training procedure. Toward this end we develop a relevance feedback approach based on the concept of incremental learning developed recently in the theory of support vector machines. The proposed approach is demonstrated using clustered microcalcifications extracted from a database consisting of 76 mammograms.

In this paper the blind image deconvolution (BID) problem is solved using the Bayesian framework. In order to find the parameters of the proposed Bayesian model we present a new generalization of the expectation maximization (EM) algorithm based on the variational approximation methodology. The proposed variational-based algorithm for BID can be derived in closed form and can be implemented in the discrete Fourier domain. Thus, it is very efficient even for very large images. We demonstrate with numerical experiments that the algorithm which was derived by the variational methodology yields promising improvements as compared to previous Bayesian algorithms for BID. Furthermore, the methodology presented here is very general with potential applications to other Bayesian models for this and other imaging problems.

A maximum likelihood (ML) solution to the problem of obtaining high-resolution images from sequences of noisy, blurred, and low-resolution images is presented. In our formulation, the registration parameters of the low-resolution images, the degrading blur, and noise variance are unknown. Our algorithm has the advantage that all unknown parameters are obtained simultaneously using all of the available data. An efficient implementation is presented in the frequency domain, based on the expectation maximization (EM) algorithm. Simulations demonstrate the effectiveness of the algorithm.

In this paper two new object recognition and localization approaches are proposed in photon-limited noise. These approaches are based on ML and Bayesian impulse restoration (IR). For the ML approach, the expectation-maximization (EM) algorithm followed by non-linear filtering that highlights impulses is used. For the Bayesian approach, a novel prior that captures the impulsive nature of the desired solution is proposed and an extension of the EM algorithm is used to find the solution. The localization receiver operating characteristics (LROC) curve is used to quantify the performance of the proposed algorithms. Numerical experiments of an extensive Monte-Carlo study are presented. These experiments demonstrate that the proposed ML-IR approach is superior to traditional likelihood ratio detection approaches for this problem. Furthermore, they also demonstrate that the proposed Bayesian-IR framework outperforms its ML counterpart.

In this paper we present a new approach for clustering data. The clustering metric used is the normalized cross-correlation, also known as similarity, instead of the traditionally used Euclidean distance. The main advantage of this metric is that it depends on the signal shape rather than its amplitude. Under an assumption of an exponential probability model that has several desirable properties, the expectation-maximization (EM) framework is used to derive two iterative clustering algorithms. Numerical experiments are presented using simulated data in a dynamic positron emission topography study of the brain. Initial results demonstrate that the proposed method achieves better performance than several existing clustering methods.

While geometric attacks are one of the most challenging problems in watermarking, random bending is probably the most difficult to handle among all geometric attacks. We present a watermarking scheme based on a new deformable mesh model to combat such attacks. The distortion is corrected using the distortion field (DF) estimated by minimizing the matching error between the meshes of the original and the attacked image. A CDMA watermarking method is used for testing the proposed method, which embeds a multi-bit signature in the DCT domain and uses mesh model correction to achieve robustness. Experiments show that the proposed scheme can survive a wide range of random bending attacks.

Geometric attacks are among the most challenging problems in present day watermarking. Such attacks are very simple to implement yet they can defeat most of the existing watermarking algorithms without causing serious perceptual image distortion. In this paper we propose a new public watermarking algorithm, which is robust to such attacks. This algorithm uses a normalized with respect to affine transformation representation of the image based on the image moments. Then, a CDMA scheme is used to embed a multi-bit watermark in the discrete cosine transform domain of the normalized image. Numerical experiments are shown where the properties of the proposed algorithm are tested. These numerical experiments show that the proposed algorithm is very robust to wide range of geometric attacks.

In this work, we explore the use of a learning-based framework for retrieval of relevant mammogram images from a database, for purposes of aiding diagnoses. A fundamental issue is how to characterize the notion of similarity between images for use in assessing relevance of images in the database. We investigate the use of several learning algorithms, namely, neural networks and support vector machines, in a two-stage hierarchical learning network for predicting the perceptual similarity from similarity scores collected in human-observer studies. The proposed approach is demonstrated using microcalcification clusters extracted from a database consisting of 76 mammograms. Initial results demonstrate that the proposed two-stage hierarchical learning network outperforms a single-stage learning network.

Microcalcification (MC) clusters in mammograms can be an indicator of breast cancer. We propose, for the first time, the use of support vector machine (SVM) learning for automated detection of MCs in digitized mammograms. In the proposed framework, MC detection is formulated as a supervised-learning problem and the method of SVM is employed to develop the detection algorithm. The proposed method is developed and evaluated using a database of 76 mammograms containing 1120 MCs. To evaluate detection performance, free-response receiver operating characteristic (FROC) curves are used. Experimental results demonstrate that, when compared to several other existing methods, the proposed SVM framework offers the best performance.

We propose a new signal-detection approach for detecting brain activations from PET or fMRI images in a two-state ("on-off") neuroimaging study. We model the activation pattern as a superposition of an unknown number of circular spatial basis functions of unknown position, size, and amplitude. We determine the number of these functions and their parameters by maximum a posteriori (MAP) estimation. To maximize the posterior distribution we use a reversible jump Markov-chain Monte-Carlo (RJMCMC) algorithm. The main advantage of RJMCMC is that it can estimate parameter vectors of unknown length. Thus, in the model used the number of activation sites does not need to be known. Using a phantom derived from a neuroimaging study, we demonstrate that the proposed method can estimate more accurately the activation pattern from traditional approaches.

In this paper, we examine the problem of locating an object in an image when size and rotation are unknown. Previous work has shown that with known geometric parameters, an image restoration method can be useful by estimating a delta function at the object location. When the geometric parameters are unknown, this method becomes impractical because the likelihood surface to be minimized across size and rotation has numerous local minima and areas of zero gradient. We propose a new approach where a smooth approximation of the template is used to minimize a well-behaved likelihood surface. A coarse-to-fine approximation of the original template using a diffusion-like equation is used to create a library of templates. Using this library, we can successively perform minimizations which are locally well-behaved. As detail is added to the template, the likelihood surface gains local minima, but previous estimates place us within a well-behaved "bowl" around the global minimum, leading to an accurate estimate. Numerical experiments are shown which verify the value of this approach for a wide range of values of the geometric parameters.

In this paper, we investigate an approach based on support vector machines (SVMs) for detection of microcalcification (MC) clusters in digital mammograms, and propose a successive enhancement learning scheme for improved performance. SVM is a machine-learning method, based on the principle of structural risk minimization, which performs well when applied to data outside the training set. We formulate MC detection as a supervised-learning problem and apply SVM to develop the detection algorithm. We use the SVM to detect at each location in the image whether an MC is present or not. We tested the proposed method using a database of 76 clinical mammograms containing 1120 MCs. We use free-response receiver operating characteristic curves to evaluate detection performance, and compare the proposed algorithm with several existing methods. In our experiments, the proposed SVM framework outperformed all the other methods tested. In particular, a sensitivity as high as 94% was achieved by the SVM method at an error rate of one false-positive cluster per image. The ability of SVM to out perform several well-known methods developed for the widely studied problem of MC detection suggests that SVM is a promising technique for object detection in a medical imaging application.

A new technique for designing digital all-pass IIR filters is proposed. The approach is based on the vector space projection method. Constraint sets, and their associated projectors, that capture the properties of the desired group delay are given. Examples that demonstrate the advantages and flexibility of this method as well as comparisons with a well-known method (Nguyen et al., 1994) are furnished.

We present a new active contour algorithm to delineate vocal folds from high-speed digital recordings of the larynx. The main novelty of this algorithm is that it incorporates effectively our prior knowledge about the local spatial and temporal behavior of the vocal folds. This allows the active contours to track better the vocal folds in areas where traditionally active contour algorithms perform poorly. We present numerical examples with real data where the effectiveness of the proposed algorithm is demonstrated.

A common image processing problem is determining the location of an object using a template when the size and rotation of the target are unknown. Using a maximum likelihood formulation, localization is possible by computing a likelihood surface for a dense sampling of the size and rotation space. However, optimization is complicated by local minima and regions of small or zero gradient. We therefore demonstrate a technique which employs a library of templates starting from a smooth approximation and adding detail until the exact template is reached. Successively estimating the geometric parameters using these templates achieves the accuracy of the exact template while remaining within a well-behaved "bowl" in the search space which allows standard minimization techniques to be used.

We explore the use of various learning algorithms to predict the user's measure of similarity between a given query image and images in a database. Our aim is to obtain a similarity coefficient, for use in image retrieval, that more accurately reflects that of the user. The performance of a variety of learning machines was evaluated using statistical resampling to estimate the prediction error and retrieval effectiveness. The proposed approach was demonstrated using synthetic shape and texture examples. The results of the study are very promising, especially those obtained by the general regression neural network and the support vector machine/radial basis function method.

In this paper, we examine the restoration problem when the point-spread function (PSF) of the degradation system is partially known. For this problem, the PSF is assumed to be the sum of a known deterministic and an unknown random component. This problem has been examined before; however, in most previous works the problem of estimating the parameters that define the restoration filters was not addressed. In this paper, two iterative algorithms that simultaneously restore the image and estimate the parameters of the restoration filter are proposed using evidence analysis (EA) within the hierarchical Bayesian framework. We show that the restoration step of the first of these algorithms is in effect almost identical to the regularized constrained total least-squares (RCTLS) filter, while the restoration step of the second is identical to the linear minimum mean square-error (LMMSE) filter for this problem. Therefore, in this paper we provide a solution to the parameter estimation problem of the RCTLS filter. We further provide an alternative approach to the expectation-maximization (EM) framework to derive a parameter estimation algorithm for the LMMSE filter. These iterative algorithms are derived in the discrete Fourier transform (DFT) domain; therefore, they are computationally efficient even for large images. Numerical experiments are presented that test and compare the proposed algorithms.

Many optical flow estimation techniques are based on the differential optical flow equation. These algorithms involve solving over-determined systems of optical flow equations. Least squares (LS) estimation is usually used to solve these systems even though the underlying noise does not conform to the model implied by LS estimation. To ameliorate this problem, work has been done using the total least squares (TLS) method instead. However, the noise model presumed by TLS is again different from the noise present in the system of optical flow equations. A proper way to solve the system of optical flow equations is the constrained total least squares (CTLS) technique. The derivation and analysis of the CTLS technique for optical flow estimation is presented in this paper. It is shown that CTLS outperforms TLS and LS optical flow estimation.

In tomographic image reconstruction, it is usually assumed that the system matrix is known exactly, although this is not usually the case in practice. We investigate the potential benefit of modeling the system matrix as the sum of a known part and an unknown random error. Using some of simplifying assumptions, we develop a penalized weighted least squares (PWLS) reconstruction algorithm for this problem. Our experiments indicate that this approach can, indeed lead to significant improvements in the reconstructed image, both visually and quantitatively.

The problem of the enhancement of a low bit-rate compressed video sequence using the information provided by the encoder is investigated in this paper. The proposed algorithm is spatio-temporally adaptive and enforces different degrees of between-block, within-block, and temporal smoothness of the decompressed frames based on macroblock types. The algorithm uses the projections onto the sets that capture the information conveyed by the transmitted data to constrain the solution space. A partially automatic regularization parameter estimation algorithm is also proposed in this paper. An analysis of PSNR gain per macroblock type is presented to cast insight into the compressed video enhancement problem. The experimental results demonstrate the effectiveness of the proposed approach.

In this correspondence, a solution is developed for the regularized total least squares (RTLS) estimate in linear inverse problems where the linear operator is nonconvolutional. Our approach is based on a Rayleigh quotient (RQ) formulation of the TLS problem, and we accomplish regularization by modifying the RQ function to enforce a smooth solution. A conjugate gradient algorithm is used to minimize the modified RQ function. As an example, the proposed approach has been applied to the perturbation equation encountered in optical tomography. Simulation results show that this method provides more stable and accurate solutions than the regularized least squares and a previously reported total least squares approach, also based on the RQ formulation.

A number of restoration filters have been proposed for the restoration problem from partially-known blurs. Previously we proposed the regularized constrained least-squares filter (RCTLS) and showed that it has a number of advantages over previous ones (Mesarovic et al. 1995). However, the problem of estimating the parameters that define the RCTLS filter has not yet been addressed. In this paper we propose a two-step algorithm based on the hierarchical Bayesian approach to simultaneously restore the image and estimate the parameters of the RCTLS restoration filter. The algorithm is derived in the DFT domain; thus, it is very efficient even for very large images.

Pel-recursive motion estimation is a well established method for finding the displacement vector-field (DVF) between adjacent image frames. The motion due to the optical flow in image sequences is estimated recursively. In this paper, we improve the Wiener-based pel-recursive algorithm by using spatially-adaptive regularization. The outcome of the regularized solution is dependent upon the value of the regularization parameter. This work employs a data-driven approach called generalized cross-validation (GCV) to determine the optimal value of the regularization parameter for each pixel. Experimental results are presented and the linear minimum mean-squared (LMMSE) solution (also known as the Wiener solution) is compared to the proposed approach.

In this paper we examine the restoration problem when the point-spread function (PSF) of the degradation system, is partially known. For this problem the PSF is assumed to be the sum of a known deterministic and an unknown random component. This problem, has been examined before; however, in most previous works the problem of estimating the parameters that define the restoration, filters was not addressed. In this paper two iterative algorithms that simultaneously restore the image and estimate the parameters of the restoration filter are proposed using evidence analysis (EA) within the hierarchical Bayesian framework. Numerical experiments are presented that test and compare the proposed algorithms.

We propose a new method for disparity assisted stereo optical flow estimation. This method is based on the linearization of the round-about compatibility constraint, which converts a stereo optical flow estimation problem to a single channel optical flow estimation problem. An over-determined system of optical flow equations can then be constructed for estimating the flow fields. The total least squares, instead of the traditional least squares is used to solve the estimation problem. We also investigate the extension of the locally constant flow model across the time domain. The experiments presented demonstrate that the proposed technique performs very well.

We present some new results for multichannel recovery of compressed video. This work extends our previously proposed multichannel recovery algorithm in that: (1) it allows bi-directional motion information to be utilised in the recovery algorithm and the motion compensation can be done at a sub-pixel level; (2) a simplified version of the recovery algorithm is introduced to reduce the computational cost. Numerical simulations using H.261 and H.263 compressed video sequences are provided to demonstrate the effectiveness of the proposed algorithms.

A new technique for designing finite impulse response (FIR) quadrature mirror filters (QMFs) is proposed. The approach is based on the vector space projection method (VSPM). Convex constraint sets and their projections that capture the properties of the desired QMFs are given. The proposed approach produces equiripple filters. This method is compared with the classical Johnston's (1980) method and is shown to have certain advantages.

It has been demonstrated that object recognition can be formulated as an image-restoration problem. In this approach, which we term impulse restoration, the objective is to restore a delta function indicating the object's location. We develop solutions based on impulse restoration for the Gaussian noise case. We propose a new iterative approach, based on the expectation-maximization (EM) algorithm, that simultaneously estimates the background statistics and restores a delta function at the location of the template. We use localization-receiver-operating characteristics (LROC) curves to evaluate quantitatively the performance of this approach and compare it with existing methods. We present experimental results that demonstrate that impulse restoration is a powerful approach for detecting known objects in images severely degraded by noise. Our experiments demonstrate that accurate modeling and estimation of the background and noise statistics are essential to successful object detection.

In this study we propose a multichannel recovery approach to ameliorating artifacts in compressed video. According to this approach, regularization operators are defined to capture both spatial and temporal correlation properties in an image sequence. In particular a regularization operator is defined explicitly to enforce smoothness along the motion trajectories. In addition, a new approach is proposed for the determination of regularization parameters in the recovery algorithm utilizing the original image in the coder, unlike in traditional image restoration where they have to be estimated from the already degraded image data.

A regularized total least square (RTLS) approach to solve a linear perturbation equation encountered in optical tomography is developed based on the Rayleigh quotient formulation. To compute efficiently the solution, the Rayleigh quotient form of the RTLS filter (RQF-RTLS) is used and a conjugate gradient algorithm is implemented. Simulation results show that the RQF-RTLS method obtains more stable and accurate solutions than the regularized least squares (RLS) approach which does not account for the errors in the operator.

We present a new image recovery algorithm to remove, in addition to blocking, ringing artifacts from compressed images and video. This new algorithm is based on the theory of projections onto convex sets (POCS). A new family of directional smoothness constraint sets is defined based on line processes modeling of the image edge structure. The definition of these smoothness sets also takes into account the fact that the visibility of compression artifacts in an image is spatially varying. To overcome the numerical difficulty in computing the projections onto these sets, a divide-and-conquer (DAC) strategy is introduced. According to this strategy, new smoothness sets are derived such that their projections are easier to compute. The effectiveness of the proposed algorithm is demonstrated through numerical experiments using Motion Picture Expert Group based (MPEG-based) coders-decoders (codecs).

In this paper, we investigate the relation between the image restoration and the template matching problems. We present a new formulation for template matching that establishes the duality between these two problems. According to this formulation the restored template is used to ascertain its location. An alternative formulation is also suggested which is based on the observation that template matching can be viewed as an image restoration problem where the degraded image is blurred by a linear point spread function-the template. It is shown that, unlike image restoration, all second order statistics required for the implementation of linear minimum mean-square error (LMMSE) template matching can be accurately estimated. LMMSE template matching is subsequently applied to the block-matching based motion estimation from degraded image sequences. Our experimental results indicate that LMMSE template matching is superior to traditional block-matching.

Restoration of image sequences is an important problem that can be encountered in many image processing applications, such as visual communications, robot guidance, and target tracking. The independent restoration of each frame in an image sequence is a suboptimal approach because the between-frame correlations are not explicitly taken into consideration. In this paper we address this problem by proposing a multichannel restoration approach. The multiple time-frames (channels) of the image sequence are restored simultaneously by using a multichannel regularized least-squares formulation of the problem. The regularization operator captures both within- and between-frame (channel) properties of the image sequence with the explicit use of the displacement vector field. We propose a number of different approaches to obtain the multichannel regularization operator, as well as an algorithm to iteratively compute the restored images. We present experiments that demonstrate the value of the proposed multichannel approach.

High-order entropy coding (HOEC) has the potential to provide higher compression ratios than the usually used zero-order entropy coding (ZOEC) approaches. However, serious implementation difficulties severely limit the practical value of HOEC for grayscale image compression. We examine the bit-plane decomposition (BPD) representation as a simple alternative that bypasses some of the implementation difficulties of HOEC. We show, however, that BPD introduces undesired coding overhead when used to represent grayscale images. We therefore propose a new binary image representation called magnitude-based binary decomposition (MBBD) which avoids any coding overhead when used to represent grayscale images. Thus, MBBD both bypasses the implementation difficulties of HOEC and does not have the drawbacks of the BPD. We present numerical experiments that verify the theoretical analysis of the BPD and MBBD representations. In addition, our experiments demonstrate that MBBD-HOEC yields better results than ZOEC for lossy image compression and is also very effective for progressive image transmission.

An iterative maximum a posteriori (MAP) algorithm is proposed for simultaneous signal-covariance estimation and restoration when only partial knowledge of the system response matrix (SRM) and the noisy-blurred sinogram of an image to be reconstructed are available. Convergence analysis is performed to ascertain that the proposed covariance estimator converges to the optimal one in the MAP sense. The superiority of the proposed algorithm, in comparison with the iterative linear minimum mean-squared-error (LMMSE) filter for incorrect SRM information, is experimentally verified.

In this paper, the problem of restoring an image distorted by a linear space-invariant (LSI) point-spread function (PSF) that is not exactly known is formulated as the solution of a perturbed set of linear equations. The regularized constrained total least-squares (RCTLS) method is used to solve this set of equations. Using the diagonalization properties of the discrete Fourier transform (DFT) for circulant matrices, the RCTLS estimate is computed in the DFT domain. This significantly reduces the computational cost of this approach and makes its implementation possible even for large images. An error analysis of the RCTLS estimate, based on the mean-squared-error (MSE) criterion, is performed to verify its superiority over the constrained total least-squares (CTLS) estimate. Numerical experiments for different errors in the PSF are performed to test the RCTLS estimator. Objective and visual comparisons are presented with the linear minimum mean-squared-error (LMMSE) and the regularized least-squares (RLS) estimator. Our experiments show that the RCTLS estimator reduces significantly ringing artifacts around edges as compared to the two other approaches.

At the present time, block-transform coding is probably the most popular approach for image compression. For this approach, the compressed images are decoded using only the transmitted transform data. We formulate image decoding as an image recovery problem. According to this approach, the decoded image is reconstructed using not only the transmitted data but, in addition, the prior knowledge that images before compression do not display between-block discontinuities. A spatially adaptive image recovery algorithm is proposed based on the theory of projections onto convex sets. Apart from the data constraint set, this algorithm uses another new constraint set that enforces between-block smoothness. The novelty of this set is that it captures both the local statistical properties of the image and the human perceptual characteristics. A simplified spatially adaptive recovery algorithm is also proposed, and the analysis of its computational complexity is presented. Numerical experiments are shown that demonstrate that the proposed algorithms work better than both the JPEG deblocking recommendation and our previous projection-based image decoding approach.

In this paper the problem of restoring an image distorted by a linear space-invariant (LST) point-spread function (PSF) which is not exactly known is solved using a maximum-a posteriori (MAP) formulation. Using the diagonalization properties of the discrete Fourier transform (DFT) for circulant matrices, the MAP estimate is computed in the DFT domain. The similarities between the MAP and the regularized constrained total least-squares (RCTLS) estimates are reported and their equivalence under certain conditions is discussed. A perturbation analysis of the MAP estimate is performed to obtain its mean-squared error (MSE) in a closed form, for small PSF errors. Numerical experiments for different PSF errors are performed to test the MAP estimator for this problem. Objective MSE-based and visual comparisons with the modified linear minimum mean-squared error (LMMSE) filter are presented that verify the superiority of the MAP estimator for higher PSF errors.>

In applications that demand highly detailed images, it is often not feasible nor sometimes possible to acquire images of such high resolution by just using hardware (high precision optics and charge coupled devices (CCDs)). Instead, image processing methods may be used to construct a high resolution image from multiple, degraded, low resolution images. It is assumed that the low resolution images have been sub-sampled and displaced by sub-pixel shifts. Therefore, the problem can be divided into three sub-problems: registration (estimating the shifts), restoration, and interpolation. This paper focuses on solving the first two sub-problems simultaneously, using the expectation-maximization (EM) algorithm. Experimental results are presented that demonstrate the effectiveness of this approach.>

In this paper we present a new non-linear image recovery algorithm which is based on the theory of projections onto convex sets (POCS) to reconstruct compressed images. We introduce a new family of convex smoothness constraint sets. These sets are based on the concept of the line process which models explicitly the edge structure of images and thus can eliminate both ringing and blocking coding artifacts. We also introduce a divide-and-conquer (DAC) strategy to compute the projections onto the new smoothness sets efficiently. Finally, we present experiments that demonstrate the effectiveness of the new smoothness constraint sets.>

We present a gradient-projection algorithm for solving the classical blind deconvolution problem. In our approach all known a priori information about both the unknown source and blurring functions is expressed via constraint sets. In computer simulations, the algorithm performed well even when the prior information was not accurate. In this study the algorithm is also compared with a conjugate gradient algorithm proposed by Lane (see J. Opt. Soc. Am. A, vol.9, no.9, p.1508-1514, 1992).>

Information theory indicates that coding efficiency can be improved by utilizing high-order entropy coding (HOEC). However, serious implementation difficulties limit the practical value of HOEC for grayscale image compression. We present a new approach, called binary-decomposed (BD) high-order entropy coding, that significantly reduces the complexity of the implementation and increases the accuracy in estimating the statistical model. In this approach a grayscale image is first decomposed into a group of binary sub-images, each corresponding to one of the gray levels. When HOEC is applied to these sub-images instead of the original image, the subsequent coding is made simpler and more accurate statistically. We apply this coding technique in lossless compression of medical images and imaging data, and demonstrate that the performance advantage of this approach is significant.>

We present a new matrix vector formulation of a wavelet-based subband decomposition. This formulation allows for the decomposition of both the convolution operator and the signal in the subband domain. With this approach, any single channel linear space-invariant filtering problem can be cast into a multichannel framework. We apply this decomposition to the linear space-invariant image restoration problem and propose a family of multichannel linear minimum mean square error (LMMSE) restoration filters. These filters explicitly incorporate both within and between subband (channel) relations of the decomposed image. Since only within channel stationarity is assumed in the image model, this approach presents a new method for modeling the nonstationarity of images. Experimental results are presented which test the proposed multichannel LMMSE filters. These experiments show that if accurate estimates of the subband statistics are available, the proposed multichannel filters provide major improvements over the traditional single channel filters.

The recent advances in visual communications make restoration of image sequences an increasingly important problem. In addition, this problem finds applications in other fields such as robot guidance and target tracking. Restoring the individual frames of an image sequence independently is a suboptimal approach because the between frame relations of the image sequence are not explicitly incorporated into the restoration algorithm. In this paper we address this problem by proposing a family of multichannel algorithms that restore the multiple time frames (channels) simultaneously. This is accomplished by using a multichannel regularized formulation in which the regularization operator captures both within and between- frame (channel) properties of the image sequence. More specifically, this operator captures both the spatial within-frame smoothness and the temporal along the direction of the motion between-frame smoothness. We propose a number of different methods to define multichannel regularization operators and a family of algorithms to iteratively obtain the restored images. We also present experiments that demonstrate beyond any doubt that the proposed approach produces significant improvements over traditional independent frame restoration of image sequences.

In most block-transform based codecs (coder-decoder) the compressed image is reconstructed using only the transmitted data. In this paper, the reconstruction is formulated as a regularized image recovery problem where both the transmitted data and prior knowledge about the properties of the original image are used. This is accomplished by minimizing an objective function, using iterative algorithms, which captures the smoothness properties of the original image. Experimental results are presented which demonstrate that the proposed regularized algorithms yield reconstructed images with superior quality, both visually and using objective distance metrics, to that of traditional decoders that use only the transmitted transform coefficients.

Entropy coding is a well-known method for exploiting the statistical redundancy in order to compress image data. Information theory indicates that the coding efficiency can be improved by utilizing high-order entropy coding (HEC). However, due to the high complexity of the implementation and the difficulties in estimating the high-order statistics during the coding process, high-order entropy coding has not been widely used. Conditional coding of an Lth order Markov source requires 2KL code tables with 2K probabilities in each table. In this paper, we present a new approach called binary decomposed high-order entropy coding (BDHEC) that significantly reduces the complexity of implementation of HEC techniques. Furthermore, it increases the accuracy of estimating the statistical model and thus it also improves the effectiveness of HEC for practical applications. The novelty of this approach is that the K-bits, M equals 2K representation levels, grayscale image is decomposed into M binary sub-images, each corresponding to one representation level of M outcomes of pels. Since each sub-image has only two representation levels, K is reduced to 1, the smallest possible value. Thus, when high-order conditional entropy coding is applied to these sub- images instead of the original image, the implementation complexity is significantly reduced and the accuracy of estimating the statistical model is increased. Theoretical analysis and experimental results are presented, which verify the value of BDHEC.

The reconstruction of images from incomplete block discrete cosine transform (BDCT) data is examined. The problem is formulated as one of regularized image recovery. According to this formulation, the image in the decoder is reconstructed by using not only the transmitted data but also prior knowledge about the smoothness of the original image, which complements the transmitted data. Two methods are proposed for solving this regularized recovery problem. The first is based on the theory of projections onto convex sets (POCS) while the second is based on the constrained least squares (CLS) approach. For the POCS-based method, a new constraint set is defined that conveys smoothness information not captured by the transmitted BDCT coefficients, and the projection onto it is computed. For the CLS method an objective function is proposed that captures the smoothness properties of the original image. Iterative algorithms are introduced for its minimization. Experimental results are presented.>

The authors provide a general framework for performing processing of stationary multichannel (MC) signals that is linear shift-invariant within channel and shift varying across channels. Emphasis is given to the restoration of degraded signals. It is shown that, by utilizing the special structure of semiblock circulant and block diagonal matrices, MC signal processing can be easily carried out in the frequency domain. The generalization of many frequency-domain single-channel (SC) signal processing techniques to the MC case is presented. It is shown that in MC signal processing each frequency component of a signal and system is presented, respectively, by a small vector and a matrix (of size equal to the number of channels), while in SC signal processing each frequency component in both cases is a scalar.

The application of regularization to ill-conditioned problems necessitates the choice of a regularization parameter which trades fidelity to the data with smoothness of the solution. The value of the regularization parameter depends on the variance of the noise in the data. The problem of choosing the regularization parameter and estimating the noise variance in image restoration is examined. An error analysis based on an objective mean-square-error (MSE) criterion is used to motivate regularization. Two approaches for choosing the regularization parameter and estimating the noise variance are proposed. The proposed and existing methods are compared and their relationship to linear minimum-mean-square-error filtering is examined. Experiments are presented that verify the theoretical results.

An approach is based on the block discrete cosine transform (DCT). The novelty of this approach is that the transform coefficients of all image blocks are coded and transmitted in absolute magnitude order. The resulting ordered-by-magnitude transmission is accomplished without sacrificing coding efficiency by using partition priority coding. Coding and transmission are adaptive to the characteristics of each individual image. and therefore, very efficient. Another advantage of this approach is its high progression effectiveness. Since the largest transform coefficients that capture the most important characteristics of images are coded and transmitted first, this method is well suited for progressive image transmission. Further compression of the image-data is achieved by multiple distribution entropy coding, a technique based on arithmetic coding. Experiments show that the approach compares favorably with previously reported DCT and subband image codecs.

The application of regularization to ill-conditioned problems necessitates the choice of a regularizing parameter which trades fidelity to the data for smoothness of the solution. Methods based on the properties of the residuals and on the generalized cross-validation have been proposed for estimating the regularizing parameter. Alternative methods to compute the regularizing parameter are proposed. The resulting values of the regularizing parameter are compared with the values obtained from the above-mentioned methods. Furthermore, it is shown that under certain conditions all the above-mentioned methods result in the same value for the regularizing parameter. Experimental results are presented which verify theoretical results.>

The problem of multi-channel restoration using both within and between-channel deterministic information is considered. A multi-channel image is a set of image planes that exhibit cross-plane similarity. Existing optimal restoration filters for single-plane images will yield suboptimal results when applied to multi-channel images, since between-channel information is not utilized. Multi-channel least squares restoration filters are developed using two approaches, the set theoretic and the constrained optimization. A geometric interpretation of the estimates of both filters is given. Color images, that is three-channel imagery with red, green, and blue components, are considered. Constraints that capture the within and between-channel properties of color images are developed. Issues associated with the computation of the two estimates are addressed. Finally, experiments using color images are shown.>

A new DCT (discrete cosine transform) based coding method for image sequences is presented. This technique utilizes the between frame difference of the DCT coefficients which are coded and transmitted progressively according to their magnitude (large values first). This is achieved without any overhead for the position information of the ordered samples using priority progressive coding (PPC). PPC is a new method that allows the ordered transmission of data sources without any overhead for the position information. Experiments were performed to test this method. The results from these experiments show improvement over previously reported DCT based methods.>

Digital image restoration of monochrome images has been studied extensively, however, problems associated with the restoration of multichannel images still remain to be investigated. In this paper, the Wiener solution of a multichannel restoration system is presented. Using block Toeplitz to block circulant approximation, the inversion of the multichannel imaging system becomes feasible by utilizing a fast iterative matrix inversion procedure. The restoration uses both the within-channel and between-channel correlation, hence the restored result is a better estimate than the one produced by independent channel restoration. Simulations are also presented.