Related papers: Sparse polynomial interpolation: sparse recovery, …
We study the Compressed Sensing (CS) problem, which is the problem of finding the most sparse vector that satisfies a set of linear measurements up to some numerical tolerance. We introduce an $\ell_2$ regularized formulation of CS which we…
The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…
High dimensional sparse learning has imposed a great computational challenge to large scale data analysis. In this paper, we are interested in a broad class of sparse learning approaches formulated as linear programs parametrized by a {\em…
We consider optimization problems containing nonconvex quadratic functions for which semidefinite programming (SDP) relaxations often yield strong bounds. We investigate linear inequalities that outer approximate the positive semidefinite…
In this paper we aim to tackle the problem of reconstructing a high-resolution image from a single low-resolution input image, known as single image super-resolution. In the literature, sparse representation has been used to address this…
We consider the problem of super-resolving the line spectrum of a multisinusoidal signal from a finite number of samples, some of which may be completely corrupted. Measurements of this form can be modeled as an additive mixture of a…
Spreading the information over all coefficients of a representation is a desirable property in many applications such as digital communication or machine learning. This so-called antisparse representation can be obtained by solving a convex…
Super-resolution imaging aims at improving the resolution of an image by enhancing it with other images or data that might have been acquired using different imaging techniques or modalities. In this paper we consider the task of doubling,…
For years, Single Image Super Resolution (SISR) has been an interesting and ill-posed problem in computer vision. The traditional super-resolution (SR) imaging approaches involve interpolation, reconstruction, and learning-based methods.…
In this paper, we investigate in a unified way the structural properties of solutions to inverse problems. These solutions are regularized by the generic class of semi-norms defined as a decomposable norm composed with a linear operator,…
We present a fast and accurate method for dense depth reconstruction from sparsely sampled light fields obtained using a synchronized camera array. In our method, the source images are over-segmented into non-overlapping compact superpixels…
Compressed sensing of simultaneously sparse and low-rank matrices enables recovery of sparse signals from a few linear measurements of their bilinear form. One important question is how many measurements are needed for a stable…
We consider the problem of recovering polynomials that are sparse with respect to the basis of Legendre polynomials from a small number of random samples. In particular, we show that a Legendre s-sparse polynomial of maximal degree N can be…
Several learning applications require solving high-dimensional regression problems where the relevant features belong to a small number of (overlapping) groups. For very large datasets and under standard sparsity constraints, hard…
We consider the recovery of sparse signals subject to sparse interference, as introduced in Studer et al., IEEE Trans. IT, 2012. We present novel probabilistic recovery guarantees for this framework, covering varying degrees of knowledge of…
A new sparse SOS decomposition algorithm is proposed based on a new sparsity pattern, called cross sparsity patterns. The new sparsity pattern focuses on the sparsity of terms and thus is different from the well-known correlative sparsity…
Compressive sensing predicts that sufficiently sparse vectors can be recovered from highly incomplete information. Efficient recovery methods such as $\ell_1$-minimization find the sparsest solution to certain systems of equations. Random…
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…
The blind deconvolution problem amounts to reconstructing both a signal and a filter from the convolution of these two. It constitutes a prominent topic in mathematical and engineering literature. In this work, we analyze a sparse version…
Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well…