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Recovery algorithms play a key role in compressive sampling (CS). Most of current CS recovery algorithms are originally designed for one-dimensional (1D) signal, while many practical signals are two-dimensional (2D). By utilizing 2D…

Recently, it has been discovered that results on universal sampling discretization of the square norm are useful in sparse sampling recovery with error being measured in the square norm. It was established that a simple greedy type…

Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…

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…

In this article, we discuss a novel greedy algorithm for the recovery of compressive sampled signals under noisy conditions. Most of the greedy recovery algorithms proposed in the literature require sparsity of the signal to be known or…

We address the problem of joint sparsity pattern recovery based on low dimensional multiple measurement vectors (MMVs) in resource constrained distributed networks. We assume that distributed nodes observe sparse signals which share the…

This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…

A greedy algorithm called Bayesian multiple matching pursuit (BMMP) is proposed to estimate a sparse signal vector and its support given $m$ linear measurements. Unlike the maximum a posteriori (MAP) support detection, which was proposed by…

We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of…

We address the problem of sparse recovery using greedy compressed sensing recovery algorithms, without explicit knowledge of the sparsity. Estimating the sparsity order is a crucial problem in many practical scenarios, e.g., wireless…

We consider the greedy algorithms for the joint recovery of high-dimensional sparse signals based on the block multiple measurement vector (BMMV) model in compressed sensing (CS). To this end, we first put forth two versions of simultaneous…

State-of-the-art algorithms for sparse subspace clustering perform spectral clustering on a similarity matrix typically obtained by representing each data point as a sparse combination of other points using either basis pursuit (BP) or…

For greedy block sparse recovery where the sparsity level is unknown, we derive a stopping condition to stop the iteration process. Focused on the block orthogonal matching pursuit (BOMP) algorithm, we model the energy of residual signals…

Sparse signal recoveries from multiple measurement vectors (MMV) with joint sparsity property have many applications in signal, image, and video processing. The problem becomes much more involved when snapshots of the signal matrix are…

Greedy first-order methods, such as coordinate descent with Gauss-Southwell rule or matching pursuit, have become popular in optimization due to their natural tendency to propose sparse solutions and their refined convergence guarantees. In…

Matching pursuit, especially its orthogonal version (OMP) and variations, is a greedy algorithm widely used in signal processing, compressed sensing, and sparse modeling. Inspired by constrained sparse signal recovery, this paper proposes a…

Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic…

This paper is a direct followup of the recent author's paper. In this paper we continue to analyze approximation and recovery properties with respect to systems satisfying universal sampling discretization property and a special…

It has been found that radar returns of extended targets are not only sparse but also exhibit a tendency to cluster into randomly located, variable sized groups. However, the standard techniques of Compressive Sensing as applied in radar…

The realisation of sensing modalities based on the principles of compressed sensing is often hindered by discrepancies between the mathematical model of its sensing operator, which is necessary during signal recovery, and its actual…