Related papers: Convolutional Sparse Coding with Overlapping Group…

Growing evidence indicates that only a sparse subset from a pool of sensory neurons is active for the encoding of visual stimuli at any instant in time. Traditionally, to replicate such biological sparsity, generative models have been using…

Over the past decade, the celebrated sparse representation model has achieved impressive results in various signal and image processing tasks. A convolutional version of this model, termed convolutional sparse coding (CSC), has been…

This work addresses the robust reconstruction problem of a sparse signal from compressed measurements. We propose a robust formulation for sparse reconstruction which employs the $\ell_1$-norm as the loss function for the residual error and…

We consider a class of sparse learning problems in high dimensional feature space regularized by a structured sparsity-inducing norm which incorporates prior knowledge of the group structure of the features. Such problems often pose a…

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…

Sparse representations of images are useful in many computer vision applications. Sparse coding with an $l_1$ penalty and a learned linear dictionary requires regularization of the dictionary to prevent a collapse in the $l_1$ norms of the…

We consider the problem of learning a sparse graph under the Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the Laplacian constrained precision matrix. Like in…

Deepening and widening convolutional neural networks (CNNs) significantly increases the number of trainable weight parameters by adding more convolutional layers and feature maps per layer, respectively. By imposing inter- and intra-group…

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…

Sparse representation learning has recently gained a great success in signal and image processing, thanks to recent advances in dictionary learning. To this end, the $\ell_0$-norm is often used to control the sparsity level. Nevertheless,…

The $\ell_{1\text{-}2}$ regularization method has a strong sparsity promoting capability in approaching sparse solutions of linear inverse problems and gained successful applications in various mathematics and applied science fields. This…

The $\ell_1$ norm is the tight convex relaxation for the $\ell_0$ "norm" and has been successfully applied for recovering sparse signals. For problems with fewer samplings, one needs to enhance the sparsity by nonconvex penalties such as…

While convolutional sparse representations enjoy a number of useful properties, they have received limited attention for image reconstruction problems. The present paper compares the performance of block-based and convolutional sparse…

The constrained $\ell_0$ regularization plays an important role in sparse reconstruction. A widely used approach for solving this problem is the penalty method, of which the least square penalty problem is a special case. However, the…

The least-square regression problems or inverse problems have been widely studied in many fields such as compressive sensing, signal processing, and image processing. To solve this kind of ill-posed problems, a regularization term (i.e.,…

We consider the decomposition of a signal over an overcomplete set of vectors. Minimization of the $\ell^1$-norm of the coefficient vector can often retrieve the sparsest solution (so-called "$\ell^1/\ell^0$-equivalence"), a generally…

In compressed sensing, in order to recover a sparse or nearly sparse vector from possibly noisy measurements, the most popular approach is $\ell_1$-norm minimization. Upper bounds for the $\ell_2$- norm of the error between the true and…

This paper develops a convex approach for sparse one-dimensional deconvolution that improves upon L1-norm regularization, the standard convex approach. We propose a sparsity-inducing non-separable non-convex bivariate penalty function for…

Recently, penalties promoting signals that are sparse within and across groups have been proposed. In this letter, we propose a generalization that allows to encode more intricate dependencies within groups. However, this complicates the…

In many linear regression problems, including ill-posed inverse problems in image restoration, the data exhibit some sparse structures that can be used to regularize the inversion. To this end, a classical path is to use $\ell_{12}$ block…