相关论文: Une v\'eritable approche $\ell_0$ pour l'apprentis…

The sparsity of natural signals and images in a transform domain or dictionary has been extensively exploited in several applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis…

Despite its nonconvex nature, $\ell_0$ sparse approximation is desirable in many theoretical and application cases. We study the $\ell_0$ sparse approximation problem with the tool of deep learning, by proposing Deep $\ell_0$ Encoders. Two…

We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…

Recovering corrupted images is one of the most challenging problems in image processing. Among various restoration tasks, blind image deblurring has been extensively studied due to its practical importance and inherent difficulty. In this…

This paper considers the fundamental problem of learning a complete (orthogonal) dictionary from samples of sparsely generated signals. Most existing methods solve the dictionary (and sparse representations) based on heuristic algorithms,…

Finding the sparse solution of an underdetermined system of linear equations has many applications, especially, it is used in Compressed Sensing (CS), Sparse Component Analysis (SCA), and sparse decomposition of signals on overcomplete…

We consider a class of $\ell_0$-regularized linear-quadratic (LQ) optimal control problems. This class of problems is obtained by augmenting a penalizing sparsity measure to the cost objective of the standard linear-quadratic regulator…

This paper considers solving the unconstrained $\ell_q$-norm ($0\leq q<1$) regularized least squares ($\ell_q$-LS) problem for recovering sparse signals in compressive sensing. We propose two highly efficient first-order algorithms via…

In this paper we study the sparse coding problem in the context of sparse dictionary learning for image recovery. To this end, we consider and compare several state-of-the-art sparse optimization methods constructed using the shrinkage…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the…

Motivated by problems in optimization we study the sparsity of the solutions to systems of linear Diophantine equations and linear integer programs, i.e., the number of non-zero entries of a solution, which is often referred to as the…

We consider the analysis operator and synthesis dictionary learning problems based on the the $\ell_1$ regularized sparse representation model. We reveal the internal relations between the $\ell_1$-based analysis model and synthesis model.…

The most widely used form of convolutional sparse coding uses an $\ell_1$ regularization term. While this approach has been successful in a variety of applications, a limitation of the $\ell_1$ penalty is that it is homogeneous across the…

Over the past decade, learning a dictionary from input images for sparse modeling has been one of the topics which receive most research attention in image processing and compressed sensing. Most existing dictionary learning methods…

Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image…

Signal estimation problems with smoothness and sparsity priors can be naturally modeled as quadratic optimization with $\ell_0$-"norm" constraints. Since such problems are non-convex and hard-to-solve, the standard approach is, instead, to…

Recent studies of under-determined linear systems of equations with sparse solutions showed a great practical and theoretical efficiency of a particular technique called $\ell_1$-optimization. Seminal works \cite{CRT,DOnoho06CS} rigorously…

Sparse learning has recently received increasing attention in many areas including machine learning, statistics, and applied mathematics. The mixed-norm regularization based on the l1q norm with q>1 is attractive in many applications of…

Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…

Sparse coding techniques for image processing traditionally rely on a processing of small overlapping patches separately followed by averaging. This has the disadvantage that the reconstructed image no longer obeys the sparsity prior used…