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Many applications have benefited remarkably from low-dimensional models in the recent decade. The fact that many signals, though high dimensional, are intrinsically low dimensional has given the possibility to recover them stably from a…
Nonlinear sparse sensing (NSS) techniques have been adopted for realizing compressive sensing (CS) in many applications such as Radar imaging and sparse channel estimation. Unlike the NSS, in this paper, we propose an adaptive sparse…
In this paper, based on a successively accuracy-increasing approximation of the $\ell_0$ norm, we propose a new algorithm for recovery of sparse vectors from underdetermined measurements. The approximations are realized with a certain class…
A well-known analysis of Tropp and Gilbert shows that orthogonal matching pursuit (OMP) can recover a k-sparse n-dimensional real vector from 4 k log(n) noise-free linear measurements obtained through a random Gaussian measurement matrix…
Recently, many practical algorithms have been proposed to recover the sparse signal from fewer measurements. Orthogonal matching pursuit (OMP) is one of the most effective algorithm. In this paper, we use the restricted isometry property to…
In this paper we introduce a nonuniform sparsity model and analyze the performance of an optimized weighted $\ell_1$ minimization over that sparsity model. In particular, we focus on a model where the entries of the unknown vector fall into…
Non-negative blind source separation (BSS) has raised interest in various fields of research, as testified by the wide literature on the topic of non-negative matrix factorization (NMF). In this context, it is fundamental that the sources…
Binary 0-1 measurement matrices, especially those from coding theory, were introduced to compressed sensing (CS) recently. Good measurement matrices with preferred properties, e.g., the restricted isometry property (RIP) and nullspace…
We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
We study a sparse negative binomial regression (NBR) for count data by showing the non-asymptotic advantages of using the elastic-net estimator. Two types of oracle inequalities are derived for the NBR's elastic-net estimates by using the…
Most compressed sensing algorithms do not account for the effect of saturation in noisy compressed measurements, though saturation is an important consequence of the limited dynamic range of existing sensors. The few algorithms that handle…
In this paper, we study the problem of sparse vector recovery at the fusion center of a sensor network from linear sensor measurements when there is missing data. In the presence of missing data, the random sampling approach employed in…
Many regularization schemes for high-dimensional regression have been put forward. Most require the choice of a tuning parameter, using model selection criteria or cross-validation schemes. We show that a simple non-negative or…
Recent results in compressed sensing show that, under certain conditions, the sparsest solution to an underdetermined set of linear equations can be recovered by solving a linear program. These results either rely on computing sparse…
We address the exact recovery of a k-sparse vector in the noiseless setting when some partial information on the support is available. This partial information takes the form of either a subset of the true support or an approximate subset…
In this paper, we address the sparse multiple measurement vector (MMV) problem where the objective is to recover a set of sparse nonzero row vectors or indices of a signal matrix from incomplete measurements. Ideally, regardless of the…
In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In several applications the…
This article provides a new type of analysis of a compressed-sensing based technique for recovering column-sparse matrices, namely minimization of the $\ell_{1,2}$-norm. Rather than providing conditions on the measurement matrix which…
Sparse recovery aims to reconstruct an unknown spare or approximately sparse signal from significantly few noisy incoherent linear measurements. As a kind of computable incoherence measure of the measurement matrix, $q$-ratio constrained…
We demonstrate a simple greedy algorithm that can reliably recover a d-dimensional vector v from incomplete and inaccurate measurements x. Here our measurement matrix is an N by d matrix with N much smaller than d. Our algorithm,…