In this paper we propose the use of the Hyperbolic Secant (HS) distribution as a prior for the Blind Image Deconvolution (BID) problem. It is well-known that when high-pass filters are applied to natural images, the resulting coefficients are sparse. We leverage this property using the HS distribution, a seldom explored Super Gaussian distribution with suitable properties for this problem. Using the Pólya-Gamma distribution, we derive an explicit Gaussian Scale Mixture representation. This representation is then used to propose a novel variational Bayesian algorithm that outperforms state-of-the-art BID methods.

This paper proposes a deep learning model for robust image restoration when the degradation is not precisely known. We show how the Moore-Penrose pseudo-inverse of a blur convolution operator can be approximated by a Wiener filter’s impulse response. The image restoration problem is then cast as the learning of a residual on the frequencies where the blurring filter is zero which, when added to the Wiener restoration, will satisfy the image formation model. A Dynamic Filter Network removes artifacts introduced by inaccurate blur estimations and other image formation model inconsistencies. The experiments conducted on synthetic and real image datasets assert the performance and robustness of the proposed method and show its superiority to existing ones.

Most whole-slide histological images are stained with two or more chemical dyes. Slide stain separation or color deconvolution is a crucial step within the digital pathology workflow. In this paper, the blind color deconvolution problem is formulated within the Bayesian framework. Starting from a multi-stained histological image, our model takes into account both spatial relations among the concentration image pixels and similarity between a given reference color-vector matrix and the estimated one. Using Variational Bayes inference, three efficient new blind color deconvolution methods are proposed which provide automated procedures to estimate all the model parameters in the problem. A comparison with classical and current state-of-the-art color deconvolution algorithms using real images has been carried out demonstrating the superiority of the proposed approach.

Whole-slide histological images are routinely used by medical doctors in diagnosis. Most of these images are stained with the very common and inexpensive hematoxylin and eosin dyes. Slide stain separation and color normalization are crucial steps within the digital pathology workflow which require a previous color deconvolution step. This image processing task is not easy, especially when working with images taken from different microscopes and slides stained in different laboratories. In this paper, based on Variational Bayes inference, an efficient new blind color deconvolution method is proposed. The new model takes into account both spatial relations among image pixels and similarity to a given reference color-vector matrix. A comparison with classical and current state-of-the-art color deconvolution algorithms, using real images with known ground truth hematoxylin and eosin values, has been carried out. This comparison has demonstrated the superiority of the proposed approach.

In this work, we propose a new variational blind deconvolution method for spike and slab prior models. Soft-sparse or shrinkage priors such as the Laplace and other related Gaussian Scale Mixture priors may not be ideal sparsity promoting priors. They assign zero probability mass to events we may be interested in assigning a probability greater than zero. The truly sparse nature of the spike and slab priors allows us to discard irrelevant information in the blur estimation process, resulting in improved performance. We present an efficient inference algorithm to estimate the unknown blur kernel in the filter space, from which we estimate the final deblurred image. The VB approach we propose in this paper handles the inference in a much more efficient way than MCMC, and is more accurate than the standard mean field variational approximation. We prove the efficacy of our method by means of a series of experiments on both synthetically generated and real images.

In this paper, we propose a 1-bit Full Adder circuit built with Ballistic Deflection Transistors (BDT). BDT is a disruptive technology based on AlGaAs/InGaAs heterostructure. Different combinational circuits were successfully realized using BDT NAND gate and General Purpose Gate (GPG) structures. The developed circuit is an extension of BDT GPG and different from that of the previously implemented adder circuit. The proposed Adder consists of Sum and Carryout structures, comprising seven and five BDTs, respectively. Monte Carlo modeling of a BDT NAND Gate, which consists of associating two BDTs, has been performed and the obtained I-V characteristics were integrated with Verilog AMS to investigate the feasibility of the proposed circuit. Simulation results performed on Cadence Spectre simulator indicate the correct functionality of the proposed full adder.

In this paper, study of different digital logic circuits developed using two-BDT ballistic nanostructure is presented. New D flip-flop (DFF) based on the same nanostructure is also proposed. The logic structure comprises two ballistic deflection transistors (BDTs) that are experimentally proven to operate at Terahertz frequencies. The non-linear behavior of the BDT's transfer characteristic has been perfectly reproduced by means of Monte Carlo simulations, where a specific attention has been devoted to surface charges. An analytical model built on the results of advanced MC simulations has been integrated into a behavioral Verilog AMS module to confirm the functionality of the circuit design. The module is used to analyze operating conditions of different combinational circuits and to investigate the feasibility of DFF design using BDT nanostructure. The simulation results indicate successful operation of both combinational and sequential circuits developed using two-BDT logic structure under proper biasing of gate and source terminals. The operating voltages of the proposed DFF are estimated to be + 225mV.

Passive Millimeter Wave Images currently used to detect hidden threats suffer from low resolution, blur, and a very low signal-to-noise-ratio. These shortcomings render threat detection, both visual and automatic, very challenging. Furthermore, due to the presence of very severe noise, most of the blind image restoration methods fail to recover the system blurring kernel from a single image. In this paper we propose a robust Bayesian multiframe blind image deconvolution method that approximates the posterior distribution of the blur by a Dirichlet distribution. We show that this approach naturally incorporates the non-negativity and normalization constraints for the blur and cope well with the image noise. The performance of the proposed method is tested on both synthetic and real images.

Blind image deconvolution involves two key objectives: 1) latent image and 2) blur estimation. For latent image estimation, we propose a fast deconvolution algorithm, which uses an image prior of nondimensional Gaussianity measure to enforce sparsity and an undetermined boundary condition methodology to reduce boundary artifacts. For blur estimation, a linear inverse problem with normalization and nonnegative constraints must be solved. However, the normalization constraint is ignored in many blind image deblurring methods, mainly because it makes the problem less tractable. In this paper, we show that the normalization constraint can be very naturally incorporated into the estimation process by using a Dirichlet distribution to approximate the posterior distribution of the blur. Making use of variational Dirichlet approximation, we provide a blur posterior approximation that considers the uncertainty of the estimate and removes noise in the estimated kernel. Experiments with synthetic and real data demonstrate that the proposed method is very competitive to the state-of-the-art blind image restoration methods.

Many real classification tasks are oriented to sequence (neighbor) labeling, that is, assigning a label to every sample of a signal while taking into account the sequentiality (or neighborhood) of the samples. This is normally approached by first filtering the data and then performing classification. In consequence, both processes are optimized separately, with no guarantee of global optimality. In this work we utilize Bayesian modeling and inference to jointly learn a classifier and estimate an optimal filterbank. Variational Bayesian inference is used to approximate the posterior distributions of all unknowns, resulting in an iterative procedure to estimate the classifier parameters and the filterbank coefficients. In the experimental section we show, using synthetic and real data, that the proposed method compares favorably with other classification/filtering approaches, without the need of parameter tuning.

In recent years, kernel methods, in particular support vector machines (SVMs), have been successfully introduced to remote sensing image classification. Their properties make them appropriate for dealing with a high number of image features and a low number of available labeled spectra. The introduction of alternative approaches based on (parametric) Bayesian inference has been quite scarce in the more recent years. Assuming a particular prior data distribution may lead to poor results in remote sensing problems because of the specificities and complexity of the data. In this context, the emerging field of nonparametric Bayesian methods constitutes a proper theoretical framework to tackle the remote sensing image classification problem. This paper exploits the Bayesian modeling and inference paradigm to tackle the problem of kernel-based remote sensing image classification. This Bayesian methodology is appropriate for both finite- and infinite-dimensional feature spaces. The particular problem of active learning is addressed by proposing an incremental/active learning approach based on three different approaches: 1) the maximum differential of entropies; 2) the minimum distance to decision boundary; and 3) the minimum normalized distance. Parameters are estimated by using the evidence Bayesian approach, the kernel trick, and the marginal distribution of the observations instead of the posterior distribution of the adaptive parameters. This approach allows us to deal with infinite-dimensional feature spaces. The proposed approach is tested on the challenging problem of urban monitoring from multispectral and synthetic aperture radar data and in multiclass land cover classification of hyperspectral images, in both purely supervised and active learning settings. Similar results are obtained when compared to SVMs in the supervised mode, with the advantage of providing posterior estimates for classification and automatic parameter learning. Comparison with random sampling as well as standard active learning methods such as margin sampling and entropy-query-by-bagging reveals a systematic overall accuracy gain and faster convergence with the number of queries.

In this paper, we consider the problem of parameter estimation on the super resolution and Bayesian methodology for pansharpening using contourlet transform. The used methodology is able to incorporate prior knowledge on the expected characteristics of the multispectral images, include information on the unknown parameters in the form of hyperprior distributions and estimate the unknown parameters together with the high resolution multispectral image. The experimental results show that the proposed method not only enhances the spatial resolution of the pansharpened image, but also preserves the spectral information of the original multispectral image.

Synthetic aperture radar (SAR) imagery suffers from the speckle phenomenon. Speckle gives rise to the presence of multiplicative noise which severely degrades the observed images. It is known that logarithmically transformed speckle can be well approximated by a Gaussian distribution. In this paper we propose an algorithm for despeckling images, within the log-transformed spatial domain, using a TV prior whose model parameter is automatically determined using the Evidence Analysis within the Hierarchical Bayesian Paradigm. The effectiveness of the proposed algorithm, over both synthetically speckled and real SAR images, is studied.

Pansharpening is a technique that fuses a low resolution multispectral image and a high resolution panchromatic image, to obtain a multispectral image with the spatial resolution and quality of the panchromatic image while preserving spectral information of the multispectral image. In this paper, we present a new pansharpening method based on super-resolution and contourlet transform. The experimental results show that the proposed method not only enhances the spatial resolution of the pansharpened image, but also preserves the spectral information of the original multispectral image.

In this paper we present a new Bayesian methodology for the restoration of blurred and noisy images. Bayesian methods rely on image priors that encapsulate prior image knowledge and avoid the ill-posedness of image restoration problems. We use a spatially varying image prior utilizing a gamma-normal hyperprior distribution on the local precision parameters. This kind of hyperprior distribution, which to our knowledge has not been used before in image restoration, allows for the incorporation of information on local as well as global image variability, models correlation of the local precision parameters and is a conjugate hyperprior to the image model used in the paper. The proposed restoration technique is compared with other image restoration approaches, demonstrating its improved performance.

In this paper we propose and analyze a globally and locally adaptive super-resolution Bayesian methodology for pansharpening of multispectral images. The methodology incorporates prior knowledge on the expected characteristics of the multispectral images uses the sensor characteristics to model the observation process of both panchromatic and multispectral images and includes information on the unknown parameters in the model in the form of hyperprior distributions. Using real and synthetic data, the pansharpened multispectral images are compared with the images obtained by other pansharpening methods and their quality is assessed both qualitatively and quantitatively.

In this paper we present a new super resolution Bayesian method for pansharpening of multispectral images which: a) incorporates prior knowledge on the expected characteristics of the multispectral images, b) uses the sensor characteristics to model the observation process of both panchromatic and multispectral images, and c) performs the estimation of all the unknown parameters in the model. Using real data, the pansharpened multispectral images are compared with the images obtained by other pansharpening methods and their quality is assessed both qualitatively and quantitatively.

Following the hierarchical Bayesian framework for blind deconvolution problems, in this paper, we propose the use of simultaneous autoregressions as prior distributions for both the image and blur, and gamma distributions for the unknown parameters (hyperparameters) of the priors and the image formation noise. We show how the gamma distributions on the unknown hyperparameters can be used to prevent the proposed blind deconvolution method from converging to undesirable image and blur estimates and also how these distributions can be inferred in realistic situations. We apply variational methods to approximate the posterior probability of the unknown image, blur, and hyperparameters and propose two different approximations of the posterior distribution. One of these approximations coincides with a classical blind deconvolution method. The proposed algorithms are tested experimentally and compared with existing blind deconvolution methods.

In this paper the blind deconvolution problem is formulated using the variational framework. With its use approximations of the involved probability distributions are developed resulting in two algorithms for the estimation of the posterior distributions of the hyperparameters, the blur, and the original image. The performance of the two proposed restoration algorithms is demonstrated experimentally.

Super-resolution algorithms recover high-frequency information from a sequence of low-resolution observations. In this paper, we consider the impact of video compression on the super-resolution task. Hybrid motion-compensation and transform coding schemes are the focus, as these methods provide observations of the underlying displacement values as well as a variable noise process. We utilize the Bayesian framework to incorporate this information and fuse the super-resolution and post-processing problems. A tractable solution is defined, and relationships between algorithm parameters and information in the compressed bitstream are established. The association between resolution recovery and compression ratio is also explored. Simulations illustrate the performance of the procedure with both synthetic and nonsynthetic sequences.

We consider the problem of reconstructing a high-resolution image from an incomplete set of undersampled, shifted, degraded frames with subpixel displacement errors. We derive mathematical expressions for the calculation of the maximum a posteriori (MAP) estimate of the high resolution image given the low resolution observed images. We also examine the role played by the prior model when an incomplete set of low resolution images is used. Finally, the proposed method is tested on real and synthetic images.

In this paper we consider the estimation of the unknown hyperparameters for the problem of reconstructing a high-resolution image from multiple undersampled, shifted, blurred and degraded frames with subpixel displacement errors. We derive mathematical expressions for the iterative calculation of the maximum likelihood estimate (mle) of the unknown hyperparameters given the low resolution observed images. Finally, the proposed method is tested on a synthetic image.

In this paper, we develop a multichannel image restoration algorithm using compound Gauss-Markov random fields (CGMRF) models. The line process in the CGMRF allows the channels to share important information regarding the objects present in the scene. In order to estimate the underlying multichannel image, two new iterative algorithms are presented and their convergence is established. They can be considered as extensions of the classical simulated annealing and iterative conditional methods. Experimental results with color images demonstrate the effectiveness of the proposed approaches.

A framework for recovering high-resolution information from a sequence of sub-sampled and compressed observations is presented. Compression schemes that describe a video sequence through a combination of motion vectors and transform coefficients are the focus (e.g. the MPEG and ITU family of standards), and we consider the influence of both the motion vectors and transform coefficients within the reconstruction algorithm. A Bayesian approach is utilized to incorporate the information, and results show a discemable improvement in resolution, as compared to standard interpolation methods.

We propose a new iterative method for Maximum a Posteriori (MAP) reconstruction of SPECT (Single Photon Emission Computed Tomography) images. The method uses Compound Gauss Markov Random Fields (CGMRF) as prior model and is stochastic for the line process and deterministic for the reconstruction. Synthetic and real images are used to compare the new method with existing ones.

SPECT (single photon emission computed tomography) is used in nuclear medicine to determine the distribution of a radioactive isotope within a patient from tomographic views or projection data. These images are severely degraded due to the presence of noise and several physical factors like attenuation and scattering. We use, within the Bayesian framework, a compound Gauss Markov random field (CGMRF) as prior model to reconstruct such images. In order to find the maximum a posteriori (MAP) estimate we propose a new iterative method, which is stochastic for the line process and deterministic for the reconstruction. The proposed method is tested and compared with other reconstruction methods on both synthetic and real SPECT images.

A method for simultaneously estimating the high-resolution frames and the corresponding motion field from a compressed low-resolution video sequence is presented. The algorithm incorporates knowledge of the spatio-temporal correlation between low and high-resolution images to estimate the original high-resolution sequence from the degraded low-resolution observation. Information from the encoder is also exploited, including the transmitted motion vectors, quantization tables, coding modes and quantizer scale factors. Simulations illustrate an improvement in the peak signal-to-noise ratio when compared with traditional interpolation techniques and are corroborated with visual results.

We propose an iterative algorithm for the estimation of high resolution frames from a low resolution compressed video sequence. The algorithm exploits the existing correlation between the high and low resolution frames and the information provided by the encoder to obtain a high resolution frame. The performance of the algorithm is demonstrated experimentally.

A solution to the multichannel image restoration problem is provided using compound Gauss-Markov random fields. For the single channel deblurring problem the convergence of the simulated annealing (SA) and iterative conditional mode (ICM) algorithms has not been established. We propose two new iterative multichannel restoration algorithms which can be considered as extensions of the classical SA and ICM approaches and whose convergence is established. Experimental results with color images demonstrate the effectiveness of the proposed algorithms.

We propose an iterative algorithm for simultaneously estimating the motion field and high resolution frames from a compressed low resolution video sequence. The algorithm exploits the existing correlation between high and low resolution frames and information provided by the encoder, such as coding modes and motion vectors (when available), to obtain a higher resolution frame. The performance of the algorithm is demonstrated experimentally.

With block-based compression approaches for both still images and sequences of images annoying blocking artifacts are exhibited, primarily at high compression ratios. They are due to the independent processing (quantization) of the block transformed values of the intensity or the displaced frame difference. We propose the application of the hierarchical Bayesian paradigm to the reconstruction of block discrete cosine transform (BDCT) compressed images and the estimation of the required parameters. We derive expressions for the iterative evaluation of these parameters applying the evidence analysis within the hierarchical Bayesian paradigm. The proposed method allows for the combination of parameters estimated at the coder and decoder. The performance of the proposed algorithms is demonstrated experimentally.

In this paper, we propose the application of the hierarchical Bayesian paradigm to the image restoration problem. We derive expressions for the iterative evaluation of the two hyperparameters applying the evidence and maximum a posteriori (MAP) analysis within the hierarchical Bayesian paradigm. We show analytically that the analysis provided by the evidence approach is more realistic and appropriate than the MAP approach for the image restoration problem. We furthermore study the relationship between the evidence and an iterative approach resulting from the set theoretic regularization approach for estimating the two hyperparameters, or their ratio, defined as the regularization parameter. Finally the proposed algorithms are tested experimentally.

We use the information in the chrominance bands to reconstruct color block transformed compressed images. For the luminance and the two chrominance channels, we define a reconstruction problem and show how to estimate the unknown hyperparameters and reconstruct each band automatically. The method is tested on real images.

This paper deals with the simultaneous identification of the blur and the restoration of a noisy and blurred image. We propose the use of Dirichlet distributions to model our prior knowledge about the blurring function together with smoothness constraints on the restored image to solve the blind deconvolution problem. We show that the use of Dirichlet distributions offers a lot of flexibility in incorporating vague or very precise knowledge about the blurring process into the blind deconvolution process. The proposed MAP estimator offers additional flexibility in modeling the original image. Experimental results demonstrate the performance of the proposed algorithm.

We examine the use of compound Gauss Markov random fields (CGMRF) to restore severely blurred high range images. For this deblurring problem, the convergence of the simulated annealing (SA) and iterative conditional mode (ICM) algorithms has not been established. We propose two new iterative restoration algorithms which extend the classical SA and ICM approaches. Their convergence is established and they are tested on real and synthetic images.