Structured Sparsity

This paper deals with EEG source localization. The aim is to perform spatially coherent focal localization and recover temporal EEG waveforms, which can be useful in certain clinical applications. A new hierarchical Bayesian model is proposed with a multivariate Bernoulli Laplacian structured sparsity prior for brain activity. This distribution approximates a mixed ℓ20 pseudo norm regularization in a Bayesian framework. A partially collapsed Gibbs sampler is proposed to draw samples asymptotically distributed according to the posterior of the proposed Bayesian model. The generated samples are used to estimate the brain activity and the model hyperparameters jointly in an unsupervised framework. Two different kinds of Metropolis-Hastings moves are introduced to accelerate the convergence of the Gibbs sampler. The first move is based on multiple dipole shifts within each MCMC chain, whereas the second exploits proposals associated with different MCMC chains. Experiments with focal syn...

The low spatial resolution of hyperspectral images means that existing mixed pixels rely heavily on spectral information, making it difficult to differentiate between the target of interest and the background. The endmember extraction method is powerful in enhancing spatial structure information for hyperspectral anomaly detection, whereas most approaches are based on matrix representation, which inevitably destroys the spatial or spectral information. In this paper, we treated the hyperspectral image as a third-order tensor and proposed a novel anomaly detection method based on a low-rank linear mixing model of the scene background. The obtained abundance maps possessed more distinctive features than the raw data, which was beneficial for identifying anomalies in the background. Specifically, the low-rank tensor background was approximated as the mode-3 product of an abundance tensor and endmember matrix. Due to the distinctive features of the background’s abundance maps, we charac...

In high-dimensional statistical modeling, Generalized Linear Models (GLMs) often suffer from overfitting, multicollinearity, and error heteroscedasticity. This paper proposes a novel Bayesian hierarchical framework that leverages structured sparsity and heteroscedastic error modeling for parameter estimation in high-dimensional GLMs. We introduce a prior structure that jointly promotes group-wise sparsity and models variance heterogeneity via a heteroscedastic Gaussian scale mixture. A fully Bayesian estimation is achieved through Hamiltonian Monte Carlo (HMC), yielding interpretable and robust posterior distributions. Empirical evaluations on synthetic and real-world genomic datasets demonstrate superior performance in both predictive accuracy and variable selection compared to conventional penalized likelihood methods.

This paper presents a novel Block Iterative Bayesian Algorithm (Block-IBA) for reconstructing block-sparse signals with unknown block structures. Unlike the existing algorithms for block sparse signal recovery which assume the cluster structure of the nonzero elements of the unknown signal to be independent and identically distributed (i.i.d.), we use a more realistic Bernoulli-Gaussian hidden Markov model (BGHMM) to characterize the non-i.i.d. block-sparse signals commonly encountered in practice. The Block-IBA iteratively estimates the amplitudes and positions of the block-sparse signal using the steepest-ascent based Expectation-Maximization (EM), and optimally selects the nonzero elements of the block-sparse signal by adaptive thresholding. The global convergence of Block-IBA is analyzed and proved, and the effectiveness of Block-IBA is demonstrated by numerical experiments and simulations on synthetic and real-life data.

We propose a differentiable algorithm for image restoration inspired by the success of sparse models and self-similarity priors for natural images. Our approach builds upon the concept of joint sparsity between groups of similar image patches, and we show how this simple idea can be implemented in a differentiable architecture, allowing end-to-end training. The algorithm has the advantage of being interpretable, performing sparse decompositions of image patches, while being more parameter efficient than recent deep learning methods. We evaluate our algorithm on grayscale and color denoising, where we achieve competitive results, and on demoisaicking, where we outperform the most recent state-of-the-art deep learning model with 47 times less parameters and a much shallower architecture.

Non-local self-similarity and sparsity principles have proven to be powerful priors for natural image modeling. We propose a novel differentiable relaxation of joint sparsity that exploits both principles and leads to a general framework for image restoration which is (1) trainable end to end, (2) fully interpretable, and (3) much more compact than competing deep learning architectures. We apply this approach to denoising, blind denoising, jpeg deblocking, and demosaicking, and show that, with as few as 100K parameters, its performance on several standard benchmarks is on par or better than state-of-the-art methods that may have an order of magnitude or more parameters.

We consider a class of sparse learning problems in high dimensional feature space regularized by a structured sparsity-inducing norm that incorporates prior knowledge of the group structure of the features. Such problems often pose a considerable challenge to optimization algorithms due to the non-smoothness and non-separability of the regularization term. In this paper, we focus on two commonly adopted sparsity-inducing regularization terms, the overlapping Group Lasso penalty l 1 /l 2-norm and the l 1 /l ∞-norm. We propose a unified framework based on the augmented Lagrangian method, under which problems with both types of regularization and their variants can be efficiently solved. As one of the core building-blocks of this framework, we develop new algorithms using a partial-linearization/splitting technique and prove that the accelerated versions of these algorithms require O(1 √) iterations to obtain an-optimal solution. We compare the performance of these algorithms against that of the alternating direction augmented Lagrangian and FISTA methods on a collection of data sets and apply them to two real-world problems to compare the relative merits of the two norms.

This article presents a new method for analyzing Automatic Speech Recognition (ASR) results at the phonological feature level. To this end the Levenshtein distance algorithm is refined in order to take into account the distinctive features opposing substituted phonemes. This method allows to survey features additions or deletions, providing microscopic qualitative information as a complement to word recognition scores. To explore the relevance of the qualitative data gathered by this method, a study is conducted on a speech corpus simulating presbycusis effects on speech perception at eight severity stages. Consonantic features additions and deletions in ASR outputs are analyzed and put in relation with intelligibility data collected in 30 human subjects. ASR results show monotonic trends in most consonantic features along the degradation conditions, which appear to be consistent with the misperceptions that could be observed in human subjects.

This article presents a new method for analyzing Automatic Speech Recognition (ASR) results at the phonological feature level. To this end the Levenshtein distance algorithm is refined in order to take into account the distinctive features opposing substituted phonemes. This method allows to survey features additions or deletions, providing microscopic qualitative information as a complement to word recognition scores. To explore the relevance of the qualitative data gathered by this method, a study is conducted on a speech corpus simulating presbycusis effects on speech perception at eight severity stages. Consonantic features additions and deletions in ASR outputs are analyzed and put in relation with intelligibility data collected in 30 human subjects. ASR results show monotonic trends in most consonantic features along the degradation conditions, which appear to be consistent with the misperceptions that could be observed in human subjects.

A number of automatic lexicon construction methods have been proposed in recent years. Such approaches employ a dynamic programming (DP) match to collect statistics concerning differences between the observed phone sequence and that which was predicted by a standard lexicon. A more expressive lexicon is then constructed based upon the collected statistics for use within a speech recognition system, which offers a more accurate phone-to-word mapping. We show that the standard DP procedure leads to the introduction of spurious matches, which reduces the quality of any subsequent processing based upon the DP provided matches. In order to remove this deficiency, an iterative DP match procedure, using individual phone confusion probabilities is outlined. It was found that the iterative DP match significantly reduced the number of equiprobable matches, to the extent that for the vast majority of utterances, only one possible DP mapping resulted, thereby improving the quality of generated statistics.

In this paper, a feature extraction approach based on a three-dimensional shearlet transform (shearlet 3D) is proposed. We aim at exploiting shearlet 3D to highlight the intrinsic properties of hyperspectral images (HSIs), well known by their correlated information and high dimensionality. First, we decompose the HSI to yield coefficients arranged in cubes that help the computing of statistical parameters. Afterward, using a simultaneous orthogonal matching pursuit (SOMP) algorithm, a classification process is carried out. SOMP relies on the powerful sparse representation paradigm, which helps representing data in a low-dimensional space. It is also built over the assumption that the contextual information incorporation into the sparse recovery problem improves the classification performance. To this algorithm, we propose to add an adapted decision rule where a similarity measurement is calculated to well assign the appropriate labels to pixels of interest. Experimental results proved that our proposed method outperformed state-of-the-art classifiers. Thanks to our proposed approach, we succeeded to build discriminative descriptors reaching high overall accuracies for two different HSI datasets, without taking into account all the shearlet 3D coefficients.

Speech technology is firmly rooted in daily life, most notably in command-and-control (C&C) applications. C&C usability downgrades quickly, however, when used by people with non-standard speech. We pursue a fully adaptive vocal user interface (VUI) which can learn both vocabulary and grammar directly from interaction examples, achieving robustness against non-standard speech by building up models from scratch. This approach raises feasibility concerns on the amount of training material required to yield an acceptable recognition accuracy. In a previous work, we proposed a VUI based on non-negative matrix factorisation (NMF) to find recurrent acoustic and semantic patterns comprising spoken commands and device-specific actions, and showed its effectiveness on unimpaired speech. In this work, we evaluate the feasibility of a self-taught VUI on a new database called DOMOTICA-3, which contains dysarthric speech with typical commands in a home automation setting. Additionally, we compare our NMF-based system with a system based on Gaussian mixtures. The evaluation favours our NMF-based approach, yielding feasible recognition accuracies for people with dysarthric speech after a few learning examples. Finally, we propose the use of a multi-layered semantic frame structure and demonstrate its effectiveness in boosting overall performance.

Over the last decade, the number of digital images captured per day witnessed a massive explosion. Nevertheless, the visual quality of photographs is often degraded by noise during image acquisition or transmission. With the re-emergence of deep neural networks, the performance of image denoising techniques has been substantially improved in recent years. The objective of this paper is to provide a comprehensive survey of recent advances in image denoising techniques based on deep neural networks. In doing so, we commence with a thorough description of the fundamental preliminaries of the image denoising problem followed by highlighting the benchmark datasets and the widely used metrics for objective assessments. Subsequently, we study the existing deep denoisers in the supervised and unsupervised categories and review the technical specifics of some representative methods within each category. Last but not least, we conclude the analysis by remarking on trends and challenges in the development of better state-of-the-art algorithms and future research.

Over the last decade, the number of digital images captured per day witnessed a massive explosion. Nevertheless, the visual quality of photographs is often degraded by noise during image acquisition or transmission. With the re-emergence of deep neural networks, the performance of image denoising techniques has been substantially improved in recent years. The objective of this paper is to provide a comprehensive survey of recent advances in image denoising techniques based on deep neural networks. In doing so, we commence with a thorough description of the fundamental preliminaries of the image denoising problem followed by highlighting the benchmark datasets and the widely used metrics for objective assessments. Subsequently, we study the existing deep denoisers in the supervised and unsupervised categories and review the technical specifics of some representative methods within each category. Last but not least, we conclude the analysis by remarking on trends and challenges in the...

Almost every single image restoration problem has a closely related parameter, such as the scale factor in super-resolution, the noise level in image denoising, and the quality factor in JPEG deblocking. Although recent studies on image restoration problems have achieved great success due to the development of deep neural networks, they handle the parameter involved in an unsophisticated way. Most previous researchers either treat problems with different parameter levels as independent tasks, and train a specific model for each parameter level; or simply ignore the parameter, and train a single model for all parameter levels. The two popular approaches have their own shortcomings. The former is inefficient in computing and the latter is ineffective in performance. In this work, we propose a novel system called functional neural network (FuncNet) to solve a parametric image restoration problem with a single model. Unlike a plain neural network, the smallest conceptual element of our FuncNet is no longer a floating-point variable, but a function of the parameter of the problem. This feature makes it both efficient and effective for a parametric problem. We apply FuncNet to superresolution, image denoising, and JPEG deblocking. The experimental results show the superiority of our FuncNet on all three parametric image restoration tasks over the state of the arts.

In our previous work, a two-phase multiobjective sparse unmixing (Tp-MoSU) approach has been proposed, which settled the regularization parameter issues of the regularization unmixing methods. However, Tp-MoSU has limited performance in identifying the real endmembers from the highly noisy data in the first phase and cannot effectively exploit the spatial-contextual information in the second phase because of the similarity measure it used. To settle these two problems, a composite spectral similarity measure is first constructed by fusing the spectral correlation angle and the Euclidean distance. It is used instead of the Frobenius norm to measure the unmixing residuals in the first phase because it considers both the shape and amplitude discrepancy between two spectra simultaneously. Then, the L 2,∞ norm is used instead of the l 2 norm to measure the unmixing residuals in the second phase, and the initialization, recombination, mutation, and local search strategies are also elaborately redesigned to help reduce this new objective, based on which the unmixing tasks of all pixels in a hyperspectral image can be completed at once. Therefore, this new measure facilitates the estimation of the abundances as a whole, and thus, the spatial-contextual information can be better exploited to improve the estimated abundances. Besides, the time efficiency for abundance estimation is also greatly improved. Experimental results demonstrate that the proposed method (termed as Tp-MoSU+) outperforms Tp-MoSU in both of the two phases under heavy noise and outperforms the tested regularization algorithms in estimating the abundances.

This paper introduces a novel declipping algorithm based on constrained least-squares minimization. Digital speech signals are often sampled at 16 kHz and classic declipping algorithms fail to accurately reconstruct the signal at this sampling rate due to the scarcity of reliable samples after clipping. The Constrained Blind Amplitude Reconstruction algorithm interpolates missing data points such that the resulting function is smooth while ensuring the inferred data fall in a legitimate range. The inclusion of explicit constraints helps to guide an accurate interpolation. Evaluation of declipping performance is based on automatic speech recognition word error rate and Constrained Blind Amplitude Reconstruction is shown to outperform the current state-of-the-art declipping technology under a variety of conditions. Declipping performance in additive noise is also considered.

In this paper, a novel nonlinear technique for hyperspectral image (HSI) classification is proposed. Our approach relies on sparsely representing a test sample in terms of all of the training samples in a feature space induced by a kernel function. For each test pixel in the feature space, a sparse representation vector is obtained by decomposing the test pixel over a training dictionary, also in the same feature space, by using a kernel-based greedy pursuit algorithm. The recovered sparse representation vector is then used directly to determine the class label of the test pixel. Projecting the samples into a high-dimensional feature space and kernelizing the sparse representation improve the data separability between different classes, providing a higher classification accuracy compared to the more conventional linear sparsity-based classification algorithms. Moreover, the spatial coherency across neighboring pixels is also incorporated through a kernelized joint sparsity model, where all of the pixels within a small neighborhood are jointly represented in the feature space by selecting a few common training samples. Kernel greedy optimization algorithms are suggested in this paper to solve the kernel versions of the single-pixel and multi-pixel joint sparsity-based recovery problems. Experimental results on several HSIs show that the proposed technique outperforms the linear sparsity-based classification technique, as well as the classical support vector machines and sparse kernel logistic regression classifiers.

Medical image acquisition is often intervented by unwanted noise that corrupts the information content. This paper introduces an unsupervised medical image denoising technique that learns noise characteristics from the available images and constructs denoised images. It comprises of two blocks of data processing, viz., patch-based dictionaries that indirectly learn the noise and residual learning (RL) that directly learns the noise. The model is generalized to account for both 2D and 3D images considering different medical imaging instruments. The images are considered one-by-one from the stack of MRI/CT images as well as the entire stack is considered, and decomposed into overlapping image/volume patches. These patches are given to the patch-based dictionary learning to learn noise characteristics via sparse representation while given to the RL part to directly learn the noise properties. K-singular value decomposition (K-SVD) algorithm for sparse representation is used for trainin...

This paper addresses the problem of compressively sensing a set of temporally correlated sources, in order to achieve faithful sparse signal reconstruction from noisy multiple measurement vectors (MMV). To this end, a simple sensing mechanism is proposed, which does not require the restricted isometry property (RIP) to hold near the sparsity level, whilst it provides additional degrees of freedom to better capture and suppress the inherent sampling noise effects. In particular, a reduced set of MMVs is generated by projecting the source signals onto random vectors drawn from isotropic multivariate stable laws. Then, the correlated sparse signals are recovered from the random MMVs by means of a recently introduced sparse Bayesian learning algorithm. Experimental evaluations on synthetic data with varying number of sources, correlation values, and noise strengths, reveal the superiority of our proposed sensing mechanism, when compared against well-established RIP-based compressive sensing schemes.

Recent works show that convolutional neural network (CNN) architectures have a spectral bias towards lower frequencies, which has been leveraged for various image restoration tasks in the Deep Image Prior (DIP) framework. The benefit of the inductive bias the network imposes in the DIP framework depends on the architecture. Therefore, researchers have studied how to automate the search to determine the best-performing model. However, common neural architecture search (NAS) techniques are resource and time-intensive. Moreover, best-performing models are determined for a whole dataset of images instead of for each image independently, which would be prohibitively expensive. In this work, we first show that optimal neural architectures in the DIP framework are image-dependent. Leveraging this insight, we then propose an image-specific NAS strategy for the DIP framework that requires substantially less training than typical NAS approaches, effectively enabling image-specific NAS. We justify the proposed strategy's effectiveness by (1) demonstrating its performance on a NAS Dataset for DIP that includes 522 models from a particular search space (2) conducting extensive experiments on image denoising, inpainting, and super-resolution tasks. Our experiments show that image-specific metrics can reduce the search space to a small cohort of models, of which the best model outperforms current NAS approaches for image restoration. Codes and datasets are available at https://github.com/ozgurkara99/ISNAS-DIP.

Structured sparsity has recently emerged in statistics, machine learning and signal processing as a promising paradigm for learning in high-dimensional settings. All existing methods for learning under the assumption of structured sparsity rely on prior knowledge on how to weight (or how to penalize) individual subsets of variables during the subset selection process, which is not available in general. Inferring group weights from data is a key open research problem in structured sparsity. In this paper, we propose a Bayesian approach to the problem of group weight learning. We model the group weights as hyperparameters of heavy-tailed priors on groups of variables and derive an approximate inference scheme to infer these hyperparameters. We empirically show that we are able to recover the model hyperparameters when the data are generated from the model, and we demonstrate the utility of learning weights in synthetic and real denoising problems.

In this paper, we propose a hierarchical Bayesian model approximating the ℓ20 mixed-norm regularization by a multivariate Bernoulli Laplace prior to solve the EEG inverse problem by promoting spatial structured sparsity. The posterior distribution of this model is too complex to derive closed-form expressions of the standard Bayesian estimators. An MCMC method is proposed to sample this posterior and estimate the model parameters from the generated samples. The algorithm is based on a partially collapsed Gibbs sampler and a dual dipole random shift proposal for the non-zero positions. The brain activity and all other model parameters are jointly estimated in a completely unsupervised framework. The results obtained on synthetic data with controlled ground truth show the good performance of the proposed method when compared to the ℓ21 approach in different scenarios, and its capacity to estimate pointlike source activity.

Group-based sparsity models are proven instrumental in linear regression problems for recovering signals from much fewer measurements than standard compressive sensing. The main promise of these models is the recovery of "interpretable" signals through the identification of their constituent groups. In this paper, we establish a combinatorial framework for group-model selection problems and highlight the underlying tractability issues. In particular, we show that the group-model selection problem is equivalent to the well-known NP-hard weighted maximum coverage problem (WMC). Leveraging a graph-based understanding of group models, we describe group structures which enable correct model selection in polynomial time via dynamic programming. Furthermore, group structures that lead to totally unimodular constraints have tractable discrete as well as convex relaxations. We also present a generalization of the group-model that allows for within group sparsity, which can be used to model hierarchical sparsity. Finally, we study the Pareto frontier of group-sparse approximations for two tractable models, among which the tree sparsity model, and illustrate selection and computation trade-offs between our framework and the existing convex relaxations.

Unlike multispectral (MSI) and panchromatic (PAN) images, generally the spatial resolution of hyperspectral images (HSI) is limited, due to sensor limitations. In many applications, HSI with a high spectral as well as spatial resolution are required. In this paper, a new method for spatial resolution enhancement of a HSI using spectral unmixing and sparse coding (SUSC) is introduced. The proposed method fuses high spectral resolution features from the HSI with high spatial resolution features from an MSI of the same scene. Endmembers are extracted from the HSI by spectral unmixing, and the exact location of the endmembers is obtained from the MSI. This fusion process by using spectral unmixing is formulated as an ill-posed inverse problem which requires a regularization term in order to convert it into a wellposed inverse problem. As a regularizer, we employ sparse coding (SC), for which a dictionary is constructed using high spatial resolution MSI or PAN images from unrelated scenes. The proposed algorithm is applied to real Hyperion and ROSIS datasets. Compared with other state-of-the-art algorithms based on pansharpening, spectral unmixing, and SC methods, the proposed method is shown to significantly increase the spatial resolution while perserving the spectral content of the HSI. Index Terms-Fusion, hyperspectral images (HSI), multispectral images (MSI), sparse coding (SC), spectral unmixing. I. INTRODUCTION R EMOTE sensing images have been widely used in different practical applications such as earth surface monitoring, agriculture, forest monitoring, environmental studies, and military applications [1]. The main types of remote sensing images are panchromatic (PAN), multispectral (MSI), and hyperspectral images (HSI). PAN images have a high spatial resolution and spatial structures are well defined, but they are limited to one gray-scale image band. MSI have lower spatial resolution than PAN images and contain a limited number of spectral bands. HSI usually have lower spatial resolution than MSI and PAN images but have a high spectral resolution [2],

Compressive image recovery is a challenging problem that requires fast and accurate algorithms. Recently, neural networks have been applied to this problem with promising results. By exploiting massively parallel GPU processing architectures and oodles of training data, they are able to run orders of magnitude faster than existing methods. Unfortunately, these methods are difficult to train, often-times specific to a single measurement matrix, and largely unprincipled blackboxes. It was recently demonstrated that iterative sparse-signal-recovery algorithms can be “unrolled” to form interpretable deep neural networks. Taking inspiration from this work, we develop novel neural network architectures that mimic the behavior of the denoising-based approximate message passing (D-AMP) and denoising-based vector approximate message passing (D-VAMP) algorithms. We call these new networks Learned D-AMP (LDAMP) and Learned D-VAMP (LDVAMP). The LDAMP/LDVAMP networks are easy to train, can be ap...

The automatic classification of hyperspectral data is made complex by several factors, such as the high cost of true sample labeling coupled with the high number of spectral bands, as well as the spatial correlation of the spectral signature. In this paper, a transductive collective classifier is proposed for dealing with all these factors in hyperspectral image classification. The transductive inference paradigm allows us to reduce the inference error for the given set of unlabeled data, as sparsely labeled pixels are learned by accounting for both labeled and unlabeled information. The collective inference paradigm allows us to manage the spatial correlation between spectral responses of neighboring pixels, as interacting pixels are labeled simultaneously. In particular, the innovative contribution of this study includes: (1) the design of an application-specific cotraining schema to use both spectral information and spatial information, iteratively extracted at the object (set of pixels) level via collective inference; (2) the formulation of a spatial-aware example selection schema that accounts for the spatial correlation of predicted labels to augment training sets during iterative learning and (3) the investigation of a diversity class criterion that allows us to speed-up co-training classification. Experimental results validate the accuracy and efficiency of the proposed spectral-spatial, collective, cotraining strategy.

Sparse representation (SR) has been successfully used in the classification of hyperspectral images (HSIs) by representing HSI pixels over a dictionary and yielding discriminative sparse coefficients. Most of SR-based classification methods construct the dictionary by directly using some labeled pixels as atoms. Such dictionary can lead to inefficient SR for large-sized HSIs, and may be incomplete when the number of labeled pixels is less than the number of spectral bands. This paper proposes a contextual online dictionary learning (DL) method for HSIs classification, which learns a dictionary over the whole image rather than few labeled pixels. The proposed method can effectively and efficiently improve the adaptive representation capability of different pixels with an online learning mechanism. Specifically, the contextual characteristics of the HSI are integrated with discriminative spectral information for online DL, i.e., pushing similar pixels in neighborhood to share similar sparse coefficients with respect to the well-learned dictionary. By this way, the obtained sparse coefficients are structured and discriminative. Finally, a traditional classifier, i.e., the linear support vector machine, is applied to the sparse coefficients, and the final classification results are obtained. Experimental results on real HSIs show the effectiveness of the proposed method.

In this paper, a novel superpixel-based sparse representation (SSR) model is proposed for hyperspectral image (HSI) super-resolution. Specifically, given a HSI with low spatial resolution and a multispectral image (MSI) with high spatial resolution, the proposed SSR approach first learns a spectral dictionary from HSI and constructs a transformed dictionary corresponding to MSI. Then, the SSR method clusters the MSI into superpixels, whose shape and size can be adaptively adjusted according to the local structures. Since pixels within each superpixel have strong similarities, the SSR method simultaneously decomposes them on the transformed dictionary to generate the corresponding fractional abundance coefficient matrix, which can exploit the similarities within the superpixel to improve the sparse decomposition. Finally, the high resolution hyperspectral image can be reconstructed with the obtained fractional abundance coefficient matrix. Experimental results show that the proposed approach is superior to some well-known HSI super-resolution methods.

Remotely sensed hyperspectral image classification is a very challenging task due to the spatial correlation of the spectral signature and the high cost of true sample labeling. In light of this, the collective inference paradigm allows us to manage the spatial correlation between spectral responses of neighboring pixels, as interacting pixels are labeled simultaneously. The transductive inference paradigm allows us to reduce the inference error for the given set of unlabeled data, as sparsely labeled pixels are learned by accounting for both labeled and unlabeled information. In this paper, both these paradigms contribute to the definition of a spectral-relational classification methodology for imagery data. We propose a novel algorithm to assign a class to each pixel of a sparsely labeled hyperspectral image. It integrates the spectral information and the spatial correlation through an ensemble system. For every pixel of a hyperspectral image, spatial neighborhoods are constructed and used to build application-specific relational features. Classification is performed with an ensemble comprising a classifier learned by considering the available spectral information (associated with the pixel) and the classifiers learned by considering the extracted spatio-relational information (associated with the spatial neighborhoods). The more reliable labels predicted by

We use the approximate message passing framework (AMP) to address the problem of recovering a sparse vector from undersampled noisy measurements. We propose an algorithm based on Sparse Bayesian learning (SBL) . Unlike the original EM based SBL that requires matrix inversions, the proposed algorithm has linear complexity, which makes it well suited for large scale problems. Compared to other message passing techniques, the algorithm requires fewer approximations, due to the conditional Gaussian prior assumption on the original vector. Numerical results show that the proposed algorithm has comparable and in many cases better performance than existing algorithms despite significant reduction in complexity.

Intelligibility is generally accepted to be a very relevant measure in the assessment of pathological speech. In clinical practice, intelligibility is measured using one of the many existing perceptual tests. These tests usually have the drawback that they employ unnatural speech material (e.g. nonsense words) and that they cannot fully exclude errors due to the listener's bias. This raises the need for an objective and automated tool to measure intelligibility. Here, we present the Dutch Intelligibility Assessment (DIA), an objective tool that aids the speech therapist in evaluating the intelligibility of persons with pathological speech. This tool will soon be made publicly available.

Band selection is a direct and effective method to reduce the spectral dimension, which is one of popular topics in hyperspectral remote sensing. Recently, a number of methods were proposed to deal with the band selection problem. Motivated by the previous sparse representation methods, we present a novel framework for band selection based on multi-dictionary sparse representation (MDSR). By obtaining the sparse solutions for each band vector and the corresponding dictionary, the contribution of each band to the raw image is derived. In terms of contribution, the appropriate band subset is selected. Although the number of dictionaries is increasing, the efficiency of the algorithm is much higher than the previous due to the reduction of the dictionary self-learning process. Five state-of-the-art band selection methods are compared with the MDSR on three widely used hyperspectral datasets (Salinas-A, Pavia-U, and Indian Pines). Experimental results show that the MDSR achieves marginally better performance in hyperspectral image classification and better performance in average correlation coefficient and computational time. INDEX TERMS Hyperspectral image, band selection, sparse representation.

Neural networks are becoming central in several areas of computer vision and image processing and different architectures have been proposed to solve specific problems. The impact of the loss layer of neural networks, however, has not received much attention in the context of image processing: the default and virtually only choice is 2. In this paper, we bring attention to alternative choices for image restoration. In particular, we show the importance of perceptually-motivated losses when the resulting image is to be evaluated by a human observer. We compare the performance of several losses, and propose a novel, differentiable error function. We show that the quality of the results improves significantly with better loss functions, even when the network architecture is left unchanged.

Conventional pipelines for capturing, displaying, and storing images are usually defined as a series of cascaded modules, each responsible for addressing a particular problem. While this divide-and-conquer approach offers many benefits, it also introduces a cumulative error, as each step in the pipeline only considers the output of the previous step, not the original sensor data. We propose an end-to-end system that is aware of the camera and image model, enforces natural-image priors, while jointly accounting for common image processing steps like demosaicking, denoising, deconvolution, and so forth, all directly in a given output representation (e.g., YUV, DCT). Our system is flexible and we demonstrate it on regular Bayer images as well as images from custom sensors. In all cases, we achieve large improvements in image quality and signal reconstruction compared to state-of-the-art techniques. Finally, we show that our approach is capable of very efficiently handling high-resoluti...

This paper investigates a new learning formulation called structured sparsity, which is a natural extension of the standard sparsity concept in statistical learning and compressive sensing. By allowing arbitrary structures on the feature set, this concept generalizes the group sparsity idea. A general theory is developed for learning with structured sparsity, based on the notion of coding complexity associated with the structure. Moreover, a structured greedy algorithm is proposed to efficiently solve the structured sparsity problem. Experiments demonstrate the advantage of structured sparsity over standard sparsity.

Tato práce se zabývá doplňováním chybějících dat do zvukových signálů. Na úvod jsou shrnuty základní poznatky využívané dále v textu. Před samotnou aplikační částí je představena řídká reprezentace signálů a některé algoritmy jejího hledání. V kapitole věnované doplňování dat je formulován problém a krátce popsány a srovnány dosavadní metody řešení. Poté je uveden nejnovější přístup řešení využívající harmonickou strukturu signálů a provedeny experimenty. Na závěr je odvozen algoritmus pro zajištění maximální efektivity výpočtu.This thesis deals with audio inpainting problem. Firstly, basic concepts are summarized. Then, sparse representation of signals is introduced along with several algorithms. In the main part dedicated to the audio inpainting, the problem is defined and actual methods are presented and compared. The newest approach using the harmonic strucure of sound signals is then introduced, followed by several experiments and evaluation. Lastly, an algorithm ensuring the m...

Sparse representation using over-complete dictionaries have shown to produce good quality results in various image processing tasks. Dictionary learning algorithms have made it possible to engineer data adaptive dictionaries which have promising applications in image compression and image enhancement. The most common sparse dictionary learning algorithms use the techniques of matching pursuit and K-SVD iteratively for sparse coding and dictionary learning respectively. While this technique produces good results, it requires a large number of iterations to converge to an optimal solution. In this article, we use a closed form stabilized convex optimization technique for both sparse coding and dictionary learning. The approach results in providing the best possible dictionary and the sparsest representation resulting in minimum reconstruction error. Once the image is reconstructed from the compressively sensed samples, we use adaptive frequency and spatial filtering techniques to move towards exact image recovery. It is clearly seen from the results that the proposed algorithm provides much better reconstruction results than conventional sparse dictionary techniques for a fixed number of iterations. Depending inversely upon the number of details present in the image, the proposed algorithm reaches the optimal solution with a significantly lower number of iterations. Consequently, high PSNR and low MSE is obtained using the proposed algorithm for our compressive sensing framework.

Spectral unmixing is an active research area in remote sensing. The direct use of the spectral libraries in spectral unmixing is increased by increasing the availability of the libraries. In this way, the spectral unmixing problem is converted into a sparse regression problem that is time-consuming. This is due to the existence of irrelevant spectra in the library. So these spectra should be removed in some way. In this paper, a machine learning approach for spectral library pruning is introduced. At first, the spectral library is clustered based on a simple and efficient new feature space. Then the training data needed to learn a classifier are extracted by adding different noise levels to the clustered spectra. The label of the training data is determined based on the results of spectral library clustering. After learning the classifier, each pixel of the image is classified using it. For pruning the library, the spectra with the labels that none of the image pixels belong to, are removed. We use three classifiers, decision tree, neural networks and k-nearest neighbor to determine the effect of applying different classifiers. The results compared here show that the proposed method works well in noisy images.

Perceptual measurement is still the most common method for assessing disordered speech in clinical practice. The subjectivity of such a measure, strongly due to human nature, but also to its lack of interpretation with regard to local alterations in speech units, strongly motivates a sophisticated tool for objective evaluation. Of interest is the increasing performance of Deep Neural Networks in speech applications, but more importantly the fact that they are no longer considered as black boxes. The work carried out here is the first step in a long-term research project, which aims to determine the linguistic units that contribute most to the maintenance or loss of the intelligibility in speech disorders. In this context, we study a CNN trained on normal speech for a classification task of phones and tested on pathological speech. The aim of this first study is to analyze the response of the CNN model to disordered speech in order to study later its effectiveness in providing relevant knowledge in terms of speech severity or loss of intelligibility. Compared to perceptual severity and intelligibility measures, the results revealed a very strong correlation between these metrics and our classifier performance scores, which is very promising for future work.

The selection of beam orientations, which is a key step in radiation treatment planning, is particularly challenging for non-coplanar radiotherapy systems due to the large number of candidate beams. In this paper, we report progress on the group sparsity approach to beam orientation optimization, wherein beam angles are selected by solving a large scale fluence map optimization problem with an additional group sparsity penalty term that encourages most candidate beams to be inactive. The optimization problem is solved using an accelerated proximal gradient method, the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). We derive a closed-form expression for a relevant proximal operator which enables the application of FISTA. The proposed algorithm is used to create non-coplanar treatment plans for four cases (including head and neck, lung, and prostate cases), and the resulting plans are compared with clinical plans. The dosimetric quality of the group sparsity treatment plans ...

Recently, deep learning (DL) methods such as the convolutional neural networks (CNNs) have gained prominence in the area of image denoising. This is owing to their proven ability to surpass state-of-the-art classical image denoising algorithms such as BM3D. Deep denoising CNNs (DnCNNs) use many feedforward convolution layers with added regularization methods of batch normalization and residual learning to improve denoising performance significantly. However, this comes at the expense of a huge number of trainable parameters. In this paper, we address this issue by reducing the number of parameters while achieving comparable level of performance. We derive motivation from the improved performance obtained by training networks using the dense-sparse-dense (DSD) training approach. We extend this training approach to a reduced DnCNN (RDnCNN) network resulting in a faster denoising network with significantly reduced parameters and comparable performance to the DnCNN.

Conventional pipelines for capturing, displaying, and storing images are usually defined as a series of cascaded modules, each responsible for addressing a particular problem. While this divide-and-conquer approach offers many benefits, it also introduces a cumulative error, as each step in the pipeline only considers the output of the previous step, not the original sensor data. We propose an end-to-end system that is aware of the camera and image model, enforces natural-image priors, while jointly accounting for common image processing steps like demosaicking, denoising, deconvolution, and so forth, all directly in a given output representation (e.g., YUV, DCT). Our system is flexible and we demonstrate it on regular Bayer images as well as images from custom sensors. In all cases, we achieve large improvements in image quality and signal reconstruction compared to state-of-the-art techniques. Finally, we show that our approach is capable of very efficiently handling high-resoluti...

Recent works show that convolutional neural network (CNN) architectures have a spectral bias towards lower frequencies, which has been leveraged for various image restoration tasks in the Deep Image Prior (DIP) framework. The benefit of the inductive bias the network imposes in the DIP framework depends on the architecture. Therefore, researchers have studied how to automate the search to determine the best-performing model. However, common neural architecture search (NAS) techniques are resource and time-intensive. Moreover, best-performing models are determined for a whole dataset of images instead of for each image independently, which would be prohibitively expensive. In this work, we first show that optimal neural architectures in the DIP framework are image-dependent. Leveraging this insight, we then propose an image-specific NAS strategy for the DIP framework that requires substantially less training than typical NAS approaches, effectively enabling image-specific NAS. We justify the proposed strategy's effectiveness by (1) demonstrating its performance on a NAS Dataset for DIP that includes 522 models from a particular search space (2) conducting extensive experiments on image denoising, inpainting, and super-resolution tasks. Our experiments show that image-specific metrics can reduce the search space to a small cohort of models, of which the best model outperforms current NAS approaches for image restoration. Codes and datasets are available at https://github.com/ozgurkara99/ISNAS-DIP.

The increasing demand for high image quality in mobile devices brings forth the need for better computational enhancement techniques, and image denoising in particular. At the same time, the images captured by these devices can be categorized into a small set of semantic classes. However simple, this observation has not been exploited in image denoising until now. In this paper, we demonstrate how the reconstruction quality improves when a denoiser is aware of the type of content in the image. To this end, we first propose a new fully convolutional deep neural network architecture which is simple yet powerful as it achieves state-of-the-art performance even without being class-aware. We further show that a significant boost in performance of up to $0.4$ dB PSNR can be achieved by making our network class-aware, namely, by fine-tuning it for images belonging to a specific semantic class. Relying on the hugely successful existing image classifiers, this research advocates for using a ...

Hyperspectral images consist of large number of spectral bands but many of which contain redundant information. Therefore, band selection has been a common practice to reduce the dimensionality of the data space for cutting down the computational cost and alleviating from the Hughes phenomenon. This paper presents a new technique for band selection where a sparse representation of the hyperspectral image data is pursued through an existing algorithm, K-SVD, that decomposes the image data into the multiplication of an overcomplete dictionary (or signature matrix) and the coefficient matrix. The coefficient matrix, that possesses the sparsity property, reveals how importantly each band contributes in forming the hyperspectral data. By calculating the histogram of the coefficient matrix, we select the top K bands that appear more frequently than others to serve the need for dimensionality reduction and at the same time preserving the physical meaning of the selected bands. We refer to the proposed band selection algorithm based on sparse representation as SpaBS. Through experimental evaluation, we first use synthetic data to validate the sparsity property of the coefficient matrix. We then apply SpaBS on real hyperspectral data and use classification accuracy as a metric to evaluate its performance. Compared to other unsupervised band selection algorithms like PCA and ICA, SpaBS presents higher classification accuracy with a stable performance.

Distributed Compressive Sensing (DCS) is an extension of compressive sensing from single measurement vector problem to Multiple Measurement Vectors (MMV) problem. In DCS, several reconstruction algorithms have been proposed to reconstruct the joint-sparse signal ensemble. However, most of them are designed for signal ensemble sharing common support. Since the assumption of common sparsity pattern is very restrictive, we are more interested in signal ensemble containing both common and innovation components. With a goal of proposing an MMV-type algorithm that is robust to outliers (absence of common sparsity pattern), we propose Greedy Pursuits Assisted Basis Pursuit for Multiple Measurement Vectors (GPABP-MMV). It employs modified basis pursuit and MMV versions of multiple greedy pursuits. We also formulate the exact reconstruction conditions and the reconstruction error bound for GPABP-MMV. GPABP-MMV is suitable for a variety of applications including time-sequence reconstruction of video frames, reconstruction of ECG signals, etc.