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Direct imaging of exoplanets is particularly challenging due to the high contrast between the planet and the star luminosities, and their small angular separation. In addition to tailored instrumental facilities implementing adaptive optics and coronagraphy, post-processing methods combining several images recorded in pupil tracking mode are needed to attenuate the nuisances corrupting the signals of interest. Most of these post-processing methods build a model of the nuisances from the target observations themselves, resulting in strongly limited detection sensitivity at short angular separations due to the lack of angular diversity. To address this issue, we propose to build the nuisance model from an archive of multiple observations by leveraging supervised deep learning techniques. The proposed approach casts the detection problem as a reconstruction task and captures the structure of the nuisance from two complementary representations of the data. Unlike methods inspired by reference differential imaging, the proposed model is highly non-linear and does not resort to explicit image-to-image similarity measurements and subtractions. The proposed approach also encompasses statistical modelling of learnable spatial features. The latter is beneficial to improve both the detection sensitivity and the robustness against heterogeneous data. We apply the proposed algorithm to several data sets from the VLT/SPHERE instrument, and demonstrate a superior precision-recall trade-off compared to the PACO algorithm. Interestingly, the gain is especially important when the diversity induced by ADI is the most limited, thus supporting the ability of the proposed approach to learn information across multiple observations. [ABSTRACT FROM AUTHOR]

Direct imaging is an active research topic in astronomy for the detection and the characterization of young substellar objects. The very high contrast between the host star and its companions makes the observations particularly challenging. In this context, post-processing methods combining several images recorded with the pupil tracking mode of telescope are needed. In previous works, we have presented a data-driven algorithm, PACO , capturing locally the spatial correlations of the data with a multivariate Gaussian model. PACO delivers better detection sensitivity and confidence than the standard post-processing methods of the field. However, there is room for improvement due to the approximate fidelity of the PACO statistical model to the time evolving observations. In this paper, we propose to combine the statistical model of PACO with supervised deep learning. The data are first pre-processed with the PACO framework to improve the stationarity and the contrast. A convolutional neural network (CNN) is then trained in a supervised fashion to detect the residual signature of synthetic sources. Finally, the trained network delivers a detection map. The photometry of detected sources is estimated by a second CNN. We apply the proposed approach to several data sets from the VLT/SPHERE instrument. Our results show that its detection stage performs significantly better than baseline methods (cADI and PCA), and leads to a contrast improvement up to half a magnitude compared to PACO. The characterization stage of the proposed method performs on average on par with or better than the comparative algorithms (PCA and PACO) for angular separation above 0.5 arcsec. [ABSTRACT FROM AUTHOR]

Photographs captured by smartphones and mid-range cameras have limited spatial resolution and dynamic range, with noisy response in underexposed regions and color artefacts in saturated areas. This paper introduces the first approach (to the best of our knowledge) to the reconstruction of highresolution, high-dynamic range color images from raw photographic bursts captured by a handheld camera with exposure bracketing. This method uses a physically-accurate model of image formation to combine an iterative optimization algorithm for solving the corresponding inverse problem with a learned image representation for robust alignment and a learned natural image prior. The proposed algorithm is fast, with low memory requirements compared to state-of-the-art learning-based approaches to image restoration, and features that are learned end to end from synthetic yet realistic data. Extensive experiments demonstrate its excellent performance with super-resolution factors of up to ×4 on real photographs taken in the wild with hand-held cameras, and high robustness to low-light conditions, noise, camera shake, and moderate object motion. [ABSTRACT FROM AUTHOR]

A framework for color image restoration based on learning dictionaries and the K-SVD-based grayscale image denoising algorithm for sparse color image representation is presented. Results suggest that the framework is successful in color image denoising, demosaicing and inpainting.

Performing data augmentation for learning deep neural networks is known to be important for training visual recognition systems. By artificially increasing the number of training examples, it helps reducing overfitting and improves generalization. While simple image transformations can already improve predictive performance in most vision tasks, larger gains can be obtained by leveraging task-specific prior knowledge. In this work, we consider object detection, semantic and instance segmentation and augment the training images by blending objects in existing scenes, using instance segmentation annotations. We observe that randomly pasting objects on images hurts the performance, unless the object is placed in the right context. To resolve this issue, we propose an explicit context model by using a convolutional neural network, which predicts whether an image region is suitable for placing a given object or not. In our experiments, we show that our approach is able to improve object detection, semantic and instance segmentation on the PASCAL VOC12 and COCO datasets, with significant gains in a limited annotation scenario, i.e., when only one category is annotated. We also show that the method is not limited to datasets that come with expensive pixel-wise instance annotations and can be used when only bounding boxes are available, by employing weakly-supervised learning for instance masks approximation. [ABSTRACT FROM AUTHOR]

Cognitive brain imaging is accumulating datasets about the neural substrate of many different mental processes. Yet, most studies are based on few subjects and have low statistical power. Analyzing data across studies could bring more statistical power; yet the current brain-imaging analytic framework cannot be used at scale as it requires casting all cognitive tasks in a unified theoretical framework. We introduce a new methodology to analyze brain responses across tasks without a joint model of the psychological processes. The method boosts statistical power in small studies with specific cognitive focus by analyzing them jointly with large studies that probe less focal mental processes. Our approach improves decoding performance for 80% of 35 widely-different functional-imaging studies. It finds commonalities across tasks in a data-driven way, via common brain representations that predict mental processes. These are brain networks tuned to psychological manipulations. They outline interpretable and plausible brain structures. The extracted networks have been made available; they can be readily reused in new neuro-imaging studies. We provide a multi-study decoding tool to adapt to new data. Author summary: Brain-imaging findings in cognitive neuroscience often have low statistical power, despite the availability of functional imaging data across hundreds of studies. Yet, with current analytic frameworks, combining data across studies that map responses to different tasks discards the nuances of the cognitive questions they ask. In this paper, we propose a new approach for fMRI analysis, where a predictive model is used to extract the shared information from many studies together, while respecting their original paradigms. Our method extracts cognitive representations that associate a wide variety of functions to specific brain structures. This provides quantitative improvements and cognitive insights when analyzing together 35 task-fMRI studies; the breadth of the functional data we consider is much higher than in previous work. Reusing the representations learned by our approach also improves statistical power in studies outside the training corpus. [ABSTRACT FROM AUTHOR]

In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. More precisely, we interpret a large class of stochastic optimization methods as procedures that iteratively minimize a surrogate of the objective, which covers the stochastic gradient descent method and variants of the incremental approaches SAGA, SVRG, and MISO/Finito/SDCA. This point of view has several advantages: (i) we provide a simple generic proof of convergence for all of the aforementioned methods; (ii) we naturally obtain new algorithms with the same guarantees; (iii) we derive generic strategies to make these algorithms robust to stochastic noise, which is useful when data is corrupted by small random perturbations. Finally, we propose a new accelerated stochastic gradient descent algorithm and a new accelerated SVRG algorithm that is robust to stochastic noise. [ABSTRACT FROM AUTHOR]

Motivation The growing number of annotated biological sequences available makes it possible to learn genotype-phenotype relationships from data with increasingly high accuracy. When large quantities of labeled samples are available for training a model, convolutional neural networks can be used to predict the phenotype of unannotated sequences with good accuracy. Unfortunately, their performance with medium- or small-scale datasets is mitigated, which requires inventing new data-efficient approaches. Results We introduce a hybrid approach between convolutional neural networks and kernel methods to model biological sequences. Our method enjoys the ability of convolutional neural networks to learn data representations that are adapted to a specific task, while the kernel point of view yields algorithms that perform significantly better when the amount of training data is small. We illustrate these advantages for transcription factor binding prediction and protein homology detection, and we demonstrate that our model is also simple to interpret, which is crucial for discovering predictive motifs in sequences. Availability and implementation Source code is freely available at https://gitlab.inria.fr/dchen/CKN-seq. Supplementary information Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

We propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing, can notably be applied to incremental first-order methods such as the stochastic variance-reduced gradient descent algorithm and other randomized incremental optimization algorithms. QNing is also compatible with composite objectives, meaning that it has the ability to provide exactly sparse solutions when the objective involves a sparsity-inducing regularization. When combined with limited-memory BFGS rules, QNing is particularly effective at solving high-dimensional optimization problems while enjoying a worst-case linear convergence rate for strongly convex problems. We present experimental results where QNing gives significant improvements over competing methods for training machine learning methods on large samples and in high dimensions. [ABSTRACT FROM AUTHOR]

The success of deep convolutional architectures is often attributed in part to their ability to learn multiscale and invariant representations of natural signals. However, a precise study of these properties and how they affect learning guarantees is still missing. In this paper, we consider deep convolutional representations of signals; we study their invariance to translations and to more general groups of transformations, their stability to the action of diffeomorphisms, and their ability to preserve signal information. This analysis is carried by introducing a multilayer kernel based on convolutional kernel networks and by studying the geometry induced by the kernel mapping. We then characterize the corresponding reproducing kernel Hilbert space (RKHS), showing that it contains a large class of convolutional neural networks with homogeneous activation functions. This analysis allows us to separate data representation from learning, and to provide a canonical measure of model complexity, the RKHS norm, which controls both stability and generalization of any learned model. In addition to models in the constructed RKHS, our stability analysis also applies to convolutional networks with generic activations such as rectified linear units, and we discuss its relationship with recent generalization bounds based on spectral norms. [ABSTRACT FROM AUTHOR]

Admixture between populations provides opportunity to study biological adaptation and phenotypic variation. Admixture studies rely on local ancestry inference for admixed individuals, which consists of computing at each locus the number of copies that originate from ancestral source populations. Existing software packages for local ancestry inference are tuned to provide accurate results on human data and recent admixture events. Here, we introduce Loter, an open-source software package that does not require any biological parameter besides haplotype data in order to make local ancestry inference available for a wide range of species. Using simulations, we compare the performance of Loter to HAPMIX, LAMP-LD, and RFMix. HAPMIX is the only software severely impacted by imperfect haplotype reconstruction. Loter is the less impacted software by increasing admixture time when considering simulated and admixed human genotypes. For simulations of admixed Populus genotypes, Loter and LAMP-LD are robust to increasing admixture times by contrast to RFMix. When comparing length of reconstructed and true ancestry tracts, Loter and LAMP-LD provide results whose accuracy is again more robust than RFMix to increasing admixture times. We apply Loter to individuals resulting from admixture between Populus trichocarpa and Populus balsamifera and lengths of ancestry tracts indicate that admixture took place ∼100 generations ago. We expect that providing a rapid and parameter-free software for local ancestry inference will make more accessible genomic studies about admixture processes. [ABSTRACT FROM AUTHOR]

We introduce a generic scheme for accelerating gradient-based optimization methods in the sense of Nesterov. The approach, called Catalyst, builds upon the inexact accelerated proximal point algorithm for minimizing a convex objective function, and consists of approximately solving a sequence of well-chosen auxiliary problems, leading to faster convergence. One of the keys to achieve acceleration in theory and in practice is to solve these sub-problems with appropriate accuracy by using the right stopping criterion and the right warm-start strategy. We give practical guidelines to use Catalyst and present a comprehensive analysis of its global complexity. We show that Catalyst applies to a large class of algorithms, including gradient descent, block coordinate descent, incremental algorithms such as SAG, SAGA, SDCA, SVRG, MISO/Finito, and their proximal variants. For all of these methods, we establish faster rates using the Catalyst acceleration, for strongly convex and non-strongly convex objectives. We conclude with extensive experiments showing that acceleration is useful in practice, especially for ill-conditioned problems. [ABSTRACT FROM AUTHOR]

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or nonnegative, which makes our algorithm suitable for dictionary learning, sparse component analysis, and nonnegative matrix factorization. Our algorithm streams matrix columns while subsampling them to iteratively learn the matrix factors. At each iteration, the row dimension of a new sample is reduced by subsampling, resulting in lower time complexity compared to a simple streaming algorithm. Our method comes with convergence guarantees to reach a stationary point of the matrix-factorization problem. We demonstrate its efficiency on massive functional magnetic resonance imaging data (2 TB), and on patches extracted from hyperspectral images (103 GB). For both problems, which involve different penalties on rows and columns, we obtain significant speed-ups compared to state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements of a complex-valued linear transformation of the original image. Several recent phase retrieval algorithms exploit underlying sparsity of the unknown signal in order to improve recovery performance. In this work, we consider such a sparse signal prior in the context of phase retrieval, when the sparsifying dictionary is not known in advance. Our algorithm jointly reconstructs the unknown signal—possibly corrupted by noise—and learns a dictionary such that each patch of the estimated image can be sparsely represented. Numerical experiments demonstrate that our approach can obtain significantly better reconstructions for phase retrieval problems with noise than methods that cannot exploit such “hidden” sparsity. Moreover, on the theoretical side, we provide a convergence result for our method. [ABSTRACT FROM PUBLISHER]

Background: Detecting and quantifying isoforms from RNA-seq data is an important but challenging task. The problem is often ill-posed, particularly at low coverage. One promising direction is to exploit several samples simultaneously. Results: We propose a new method for solving the isoform deconvolution problem jointly across several samples. We formulate a convex optimization problem that allows to share information between samples and that we solve efficiently. We demonstrate the benefits of combining several samples on simulated and real data, and show that our approach outperforms pooling strategies and methods based on integer programming. Conclusion: Our convex formulation to jointly detect and quantify isoforms from RNA-seq data of multiple related samples is a computationally efficient approach to leverage the hypotheses that some isoforms are likely to be present in several samples. The software and source code are available at http://cbio.ensmp.fr/flipflop. [ABSTRACT FROM AUTHOR]

Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective function downhill. Such a simple principle is widely applicable and has been very popular in various scientific fields, especially in signal processing and statistics. We propose an incremental majorization-minimization scheme for minimizing a large sum of continuous functions, a problem of utmost importance in machine learning. We present convergence guarantees for nonconvex and convex optimization when the upper bounds approximate the objective up to a smooth error; we call such upper bounds "first-order surrogate functions." More precisely, we study asymptotic stationary point guarantees for nonconvex problems, and for convex ones, we provide convergence rates for the expected objective function value. We apply our scheme to composite optimization and obtain a new incremental proximal gradient algorithm with linear convergence rate for strongly convex functions. Our experiments show that our method is competitive with the state of the art for solving machine learning problems such as logistic regression when the number of training samples is large enough, and we demonstrate its usefulness for sparse estimation with nonconvex penalties. [ABSTRACT FROM AUTHOR]

Motivation: Several state-of-the-art methods for isoform identification and quantification are based on ℓ1-regularized regression, such as the Lasso. However, explicitly listing the—possibly exponentially—large set of candidate transcripts is intractable for genes with many exons. For this reason, existing approaches using the ℓ1-penalty are either restricted to genes with few exons or only run the regression algorithm on a small set of preselected isoforms.Results: We introduce a new technique called FlipFlop, which can efficiently tackle the sparse estimation problem on the full set of candidate isoforms by using network flow optimization. Our technique removes the need of a preselection step, leading to better isoform identification while keeping a low computational cost. Experiments with synthetic and real RNA-Seq data confirm that our approach is more accurate than alternative methods and one of the fastest available.Availability and implementation: Source code is freely available as an R package from the Bioconductor Web site (http://www.bioconductor.org/), and more information is available at http://cbio.ensmp.fr/flipflop.Contact: Jean-Philippe.Vert@mines.orgSupplementary information: Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

We consider supervised learning problems where the features are embedded in a graph, such as gene expressions in a gene network. In this context, it is of much interest to automatically select a subgraph with few connected components; by exploiting prior knowledge, one can indeed improve the prediction performance or obtain results that are easier to interpret. Regularization or penalty functions for selecting features in graphs have recently been proposed, but they raise new algorithmic challenges. For example, they typically require solving a combinatorially hard selection problem among all connected subgraphs. In this paper, we propose computationally feasible strategies to select a sparse and well-connected subset of features sitting on a directed acyclic graph (DAG).We introduce structured sparsity penalties over paths on a DAG called "path coding" penalties. Unlike existing regularization functions that model long-range interactions between features in a graph, path coding penalties are tractable. The penalties and their proximal operators involve path selection problems, which we efficiently solve by leveraging network flow optimization. We experimentally show on synthetic, image, and genomic data that our approach is scalable and leads to more connected subgraphs than other regularization functions for graphs. [ABSTRACT FROM AUTHOR]

The article explains the concept of parsimony which is said to be inspired from an early doctrine formulated by philosopher and theologian William of Ockham in the 14th century. Topics include the early concepts of parsimony in statistics and information theory from the 1970s and 1980s, the dictionary learning formulation, and the concept of compressed sensing and sparse recovery. Also mentioned are sparse coding and related sparse matrix factorization techniques for natural image patches.

The article focuses on dictionary learning algorithms for sparse estimation. Topics discussed include the stochastic gradient descent method, alternate minimization and block coordinate descent. Also mentioned are K-SVD algorithm, online dictionary learning and other extensions for loss functions, the square loss and other regularization functions.

The article focuses on additional computer vision applications in visual recognition. Topics discussed include action recognition in videos, visual tracking and data visualization. Also mentioned are solutions to classification problems such as local model of actions, encoding of full sequences and global model of actions.

The article focuses on the links between dictionary learning and neural networks in visual recognition. It introduces the concept of backpropagation for dictionary learning and fast approximations of sparse coding. Also mentioned is an iterative approach to approximate efficiently the solution of sparse coding problems.

The article focuses on the botany of sparse featuring coding in visual recognition. Topics discussed include local coordinate coding, laplacian sparse coding and convolutional sparse coding. Also mentioned are other variants separable sparse coding and multipath sparse coding and hierarchical matching.

The article focuses on a coding and pooling approach to image modeling in visual recognition. It presents the success of dictionary learning as an alternative to clustering techniques in bag-of-words models. Also mentioned are global pooling that discards all spatial information and local pooling that keeps part of feature matching.

The article focuses on other patch modeling approaches in image processing. Topics discussed include non-local means and non-parametric approaches, patch-based procedure BM3D for image denoising, non-local sparse methods, and Gaussian mixture models. It is noted the success of dictionary learning in image processing tasks.

The article focuses on face compression in image processing. The method encodes photographs of human faces using adaptive dictionaries, in which blocked artifacts can be reduced through a deblocking post-processing algorithm. It is suggested that each image patch can be decoded with a matrix vector multiplication and the original image can be approximated by the inverse geometrical warping.

The article focuses on image up-scaling as one of the sparse models for imaging processing. The method is also called digital zooming which is the reconstruction of high-resolution images from low-resolution images with the same sparse decomposition coefficient. Also mentioned are the new two variants such as regression formulation and bilevel optimization.

The article focuses on image denoising as one of the sparse models for imaging processing. The method is said to be formulated with an energy to minimize regularization function and the quadratic data fitting. Also mentioned are patch denoising given a fixed dictionary, from patches to full image estimation, and the use of generic versus global versus image-adaptive dictionary.

The article focuses on other matrix factorization methods in discovering the structure of natural images in sparse coding and clustering. Topics discussed include independent component analysis, non-negative matrix factorization, and archetypal analysis. Also mentioned are Bayesian models for dictionary learning and convolutional sparse coding.

The article discusses the use of structured dictionary learning in discovering the structure of natural images. The method is consist of replacing the l1-norm by a more complex sparsity-inducing penalty. Also mentioned are hierarchical structure, the topographic independent component analysis formulation, and mixture of sparse coding with a probabilistic model of latent variables.

The article discusses the technique of clustering or vector quantization in discovering the structure of natural images. The method is used for compression and communication purposes on natural image patches. It also aims to find p clusters in the data by minimizing centroids and performing alternatively exact minimization.

The article discusses principal component analysis (PCA), also known as the Karhunen-Loeve or Hotelling transform, in discovering the structure of natural images. PCA is considered as the most used unsupervised data analysis technique and a low-rank matrix factorization problem. Also mentioned is the relation between principal components and sinusoids of natural image in an asymptotic regime.

The article discusses the pre-processing scheme in discovering the structure of natural images. It describes the common practices to deal with natural image patches which include centering, contrast normalization or whitening. It also studies the effect of these practices on the image itself, and provides visual interpretation to assist the practitioner in making a choice.

The article introduces the era of modern parsimony in signal processing and statistics. It features the l1-norm and other variants which are applied to geophysics with the Lasso estimator of Tisbshirani, statistics and signal processing with basis pursuit formulation of Chen and colleagues. The era is also said to match the use of convex optimization techniques that solve feature selection or sparse decomposition problems.

We consider a class of learning problems regularized by a structured sparsity-inducing norm defined as the sum of l2- or l∞-norms over groups of variables. Whereas much effort has been put in developing fast optimization techniques when the groups are disjoint or embedded in a hierarchy, we address here the case of general overlapping groups. To this end, we present two different strategies: On the one hand, we show that the proximal operator associated with a sum of l∞-norms can be computed exactly in polynomial time by solving a quadratic min-cost flow problem, allowing the use of accelerated proximal gradient methods. On the other hand, we use proximal splitting techniques, and address an equivalent formulation with non-overlapping groups, but in higher dimension and with additional constraints. We propose efficient and scalable algorithms exploiting these two strategies, which are significantly faster than alternative approaches. We illustrate these methods with several problems such as CUR matrix factorization, multi-task learning of tree-structured dictionaries, background subtraction in video sequences, image denoising with wavelets, and topographic dictionary learning of natural image patches. [ABSTRACT FROM AUTHOR]

We consider a class of learning problems regularized by a structured sparsity-inducing norm defined as the sum of l2- or l∞-norms over groups of variables. Whereas much effort has been put in developing fast optimization techniques when the groups are disjoint or embedded in a hierarchy, we address here the case of general overlapping groups. To this end, we present two different strategies: On the one hand, we show that the proximal operator associated with a sum of l∞-norms can be computed exactly in polynomial time by solving a quadratic min-cost flow problem, allowing the use of accelerated proximal gradient methods. On the other hand, we use proximal splitting techniques, and address an equivalent formulation with non-overlapping groups, but in higher dimension and with additional constraints. We propose efficient and scalable algorithms exploiting these two strategies, which are significantly faster than alternative approaches. We illustrate these methods with several problems such as CUR matrix factorization, multi-task learning of tree-structured dictionaries, background subtraction in video sequences, image denoising with wavelets, and topographic dictionary learning of natural image patches. [ABSTRACT FROM AUTHOR]

Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved using a recently introduced tree-structured sparse regularization norm, which has proven useful in several applications. This norm leads to regularized problems that are difficult to optimize, and in this paper, we propose efficient algorithms for solving them. More precisely, we show that the proximal operator associated with this norm is computable exactly via a dual approach that can be viewed as the composition of elementary proximal operators. Our procedure has a complexity linear, or close to linear, in the number of atoms, and allows the use of accelerated gradient techniques to solve the tree-structured sparse approximation problem at the same computational cost as traditional ones using the ℓ1-norm. Our method is efficient and scales gracefully to millions of variables, which we illustrate in two types of applications: first, we consider fixed hierarchical dictionaries of wavelets to denoise natural images. Then, we apply our optimization tools in the context of dictionary learning, where learned dictionary elements naturally self-organize in a prespecified arborescent structure, leading to better performance in reconstruction of natural image patches. When applied to text documents, our method learns hierarchies of topics, thus providing a competitive alternative to probabilistic topic models. [ABSTRACT FROM AUTHOR]

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by regularizing the empirical risk with appropriate nonsmooth norms. The goal of this monograph is to present from a general perspective optimization tools and techniques dedicated to such sparsity-inducing penalties. We cover proximal methods, block-coordinate descent, reweighted ℓ2-penalized techniques, workingset and homotopy methods, as well as non-convex formulations and extensions, and provide an extensive set of experiments to compare various algorithms from a computational point of view. [ABSTRACT FROM AUTHOR]

Techniques from sparse signal representation are beginning to see significant impact in computer vision, often on nontraditional applications where the goal is not just to obtain a compact high-fidelity representation of the observed signal, but also to extract semantic information. The choice of dictionary plays a key role in bridging this gap: unconventional dictionaries consisting of, or learned from, the training samples themselves provide the key to obtaining state-of-the-art results and to attaching semantic meaning to sparse signal representations. Understanding the good performance of such unconventional dictionaries in turn demands new algorithmic and analytical techniques. This review paper highlights a few representative examples of how the interaction between sparse signal representation and computer vision can enrich both fields, and raises a number of open questions for further study. [ABSTRACT FROM AUTHOR]

Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization problem that consists of learning the basis set in order to adapt it to specific data. Variations of this problem include dictionary learning in signal processing, non-negative matrix factorization and sparse principal component analysis. In this paper, we propose to address these tasks with a new online optimization algorithm, based on stochastic approximations, which scales up gracefully to large data sets with millions of training samples, and extends naturally to various matrix factorization formulations, making it suitable for a wide range of learning problems. A proof of convergence is presented, along with experiments with natural images and genomic data demonstrating that it leads to state-of-the-art performance in terms of speed and optimization for both small and large data sets. [ABSTRACT FROM AUTHOR]

This paper presents a framework for learning multiscale sparse representations of color images and video with overcomplete dictionaries. A single-scale K-SVD algorithm was introduced in [M. Aharon, M. Elad, and A. M. Bruckstein, IEEE Trans. Signal Process., 54 (2006), pp. 4311-4322], formulating sparse dictionary learning for grayscale image representation as an optimization problem, efficiently solved via orthogonal matching pursuit (OMP) and singular value decomposition (SVD). Following this work, we propose a multiscale learned representation, obtained by using an efficient quadtree decomposition of the learned dictionary and overlapping image patches. The proposed framework provides an alternative to predefined dictionaries such as wavelets and is shown to lead to state-of-the-art results in a number of image and video enhancement and restoration applications. This paper describes the proposed framework and accompanies it by numerous examples demonstrating its strength. [ABSTRACT FROM AUTHOR]

The article focuses on face recognition in visual recognition. It presents the sparse-representation based classifier (SRC) which sparsely decomposes a set of training signals. Also mentioned are various extensions to solve the problem of face recognition which include occlusion and image misalignment.

The article focuses on the natural extensions of dictionary learning into video processing. It states that each frame should be processed independently by achieving temporal consistency between frames because of a noisy video sequence. It also suggests to adapt the inpainting and color video denoising tasks which include processing three-dimensional patches at the same time.