Related papers: Improved bounds for sparse recovery from subsample…
We study the sparse phase retrieval problem, recovering an $s$-sparse length-$n$ signal from $m$ magnitude-only measurements. Two-stage non-convex approaches have drawn much attention in recent studies for this problem. Despite…
We propose necessary and sufficient conditions for a sensing matrix to be "s-semigood" -- to allow for exact $\ell_1$-recovery of sparse signals with at most $s$ nonzero entries under sign restrictions on part of the entries. We express the…
This paper considers the use of total variation regularization in the recovery of approximately gradient sparse signals from their noisy discrete Fourier samples in the context of compressed sensing. It has been observed over the last…
We consider the problem of robustly testing the norm of a high-dimensional sparse signal vector under two different observation models. In the first model, we are given $n$ i.i.d. samples from the distribution…
In this paper, we consider the use of Total Variation (TV) minimization for compressive imaging; that is, image reconstruction from subsampled measurements. Focusing on two important imaging modalities -- namely, Fourier imaging and…
Recovering sparse vectors and low-rank matrices from noisy linear measurements has been the focus of much recent research. Various reconstruction algorithms have been studied, including $\ell_1$ and nuclear norm minimization as well as…
The achievable and converse regions for sparse representation of white Gaussian noise based on an overcomplete dictionary are derived in the limit of large systems. Furthermore, the marginal distribution of such sparse representations is…
In this paper we discuss the variable selection method from \ell0-norm constrained regression, which is equivalent to the problem of finding the best subset of a fixed size. Our study focuses on two aspects, consistency and computation. We…
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…
Detection of a signal under noise is a classical signal processing problem. When monitoring spatial phenomena under a fixed budget, i.e., either physical, economical or computational constraints, the selection of a subset of available…
We study the problem of jointly sparse support recovery with 1-bit compressive measurements in a sensor network. Sensors are assumed to observe sparse signals having the same but unknown sparse support. Each sensor quantizes its measurement…
The joint-sparse recovery problem aims to recover, from sets of compressed measurements, unknown sparse matrices with nonzero entries restricted to a subset of rows. This is an extension of the single-measurement-vector (SMV) problem widely…
Affine phase retrieval is the problem of recovering signals from the magnitude-only measurements with a priori information. In this paper, we use the $\ell_1$ minimization to exploit the sparsity of signals for affine phase retrieval,…
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…
Sparse modeling has been widely and successfully used in many applications such as computer vision, machine learning, and pattern recognition. Accompanied with those applications, significant research has studied the theoretical limits and…
In this paper, we consider a compressed sensing problem of reconstructing a sparse signal from an undersampled set of noisy linear measurements. The regularized least squares or least absolute shrinkage and selection operator (LASSO)…
In this paper we present a new algorithm for compressive sensing that makes use of binary measurement matrices and achieves exact recovery of ultra sparse vectors, in a single pass and without any iterations. Due to its noniterative nature,…
We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
Sparse signals (i.e., vectors with a small number of non-zero entries) build the foundation of most kernel (or nullspace) results, uncertainty relations, and recovery guarantees in the sparse signal processing and compressive sensing…