Related papers: What is the Largest Sparsity Pattern that Can Be R…

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…

The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…

Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…

Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem is notorious to be severe ill posed such that the recovery…

We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional…

We study the problem of approximating a matrix $\mathbf{A}$ with a matrix that has a fixed sparsity pattern (e.g., diagonal, banded, etc.), when $\mathbf{A}$ is accessed only by matrix-vector products. We describe a simple randomized…

Mixture models are widely used to fit complex and multimodal datasets. In this paper we study mixtures with high dimensional sparse latent parameter vectors and consider the problem of support recovery of those vectors. While parameter…

This work treats the recovery of sparse, binary signals through box-constrained basis pursuit using biased measurement matrices. Using a probabilistic model, we provide conditions under which the recovery of both sparse and saturated binary…

The problem of consistently estimating the sparsity pattern of a vector $\betastar \in \real^\mdim$ based on observations contaminated by noise arises in various contexts, including subset selection in regression, structure estimation in…

In this article, we review the literature on design and analysis of recursive algorithms for reconstructing a time sequence of sparse signals from compressive measurements. The signals are assumed to be sparse in some transform domain or in…

In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…

We propose a unified framework to solve general low-rank plus sparse matrix recovery problems based on matrix factorization, which covers a broad family of objective functions satisfying the restricted strong convexity and smoothness…

Consider the recovery of an unknown signal ${x}$ from quantized linear measurements. In the one-bit compressive sensing setting, one typically assumes that ${x}$ is sparse, and that the measurements are of the form…

We study the computational cost of recovering a unit-norm sparse principal component $x \in \mathbb{R}^n$ planted in a random matrix, in either the Wigner or Wishart spiked model (observing either $W + \lambda xx^\top$ with $W$ drawn from…

Sparse dictionary learning (SDL) is a fundamental technique that is useful for many image processing tasks. As an example we consider here image recovery, where SDL can be cast as a nonsmooth optimization problem. For this kind of problems,…

We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…

In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts the recovery of the phase information of a signal from…

This is the second part of a two-paper series on generalized inverses that minimize matrix norms. In Part II we focus on generalized inverses that are minimizers of entrywise p norms whose main representative is the sparse pseudoinverse for…

We consider the following k-sparse recovery problem: design an m x n matrix A, such that for any signal x, given Ax we can efficiently recover x' satisfying ||x-x'||_1 <= C min_{k-sparse} x"} ||x-x"||_1. It is known that there exist…