Related papers: Phase transition in compressed sensing using log-s…
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 investigate conditions for the unique recoverability of sparse integer-valued signals from a small number of linear measurements. Both the objective of minimizing the number of nonzero components, the so-called $\ell_0$-norm, as well as…
Numerical experiments in literature on compressed sensing have indicated that the reweighted $l_1$ minimization performs exceptionally well in recovering sparse signal. In this paper, we develop exact recovery conditions and algorithm for…
We study a class of real robust phase retrieval problems under a Gaussian assumption on the coding matrix when the received signal is sparsely corrupted by noise. The goal is to establish conditions on the sparsity under which the input…
This paper considers sequential adaptive estimation of sparse signals under a constraint on the total sensing effort. The advantage of adaptivity in this context is the ability to focus more resources on regions of space where signal…
We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and…
We initiate the study of sparse recovery problems under the Earth-Mover Distance (EMD). Specifically, we design a distribution over m x n matrices A such that for any x, given Ax, we can recover a k-sparse approximation to x under the EMD…
The sparse optimization problems arise in many areas of science and engineering, such as compressed sensing, image processing, statistical and machine learning. The $\ell_{0}$-minimization problem is one of such optimization problems, which…
We consider the question of estimating a real low-complexity signal (such as a sparse vector or a low-rank matrix) from the phase of complex random measurements. We show that in this "phase-only compressive sensing" (PO-CS) scenario, we can…
Analysis $\ell_1$-recovery refers to a technique of recovering a signal that is sparse in some transform domain from incomplete corrupted measurements. This includes total variation minimization as an important special case when the…
Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal…
Recovering an unknown complex signal from the magnitude of linear combinations of the signal is referred to as phase retrieval. We present an exact performance analysis of a recently proposed convex-optimization-formulation for this…
Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…
$\ell_1$ minimization is often used for finding the sparse solutions of an under-determined linear system. In this paper we focus on finding sharp performance bounds on recovering approximately sparse signals using $\ell_1$ minimization,…
The double sparse linear model, which has both group-wise and element-wise sparsity in regression coefficients, has attracted lots of attention recently. This paper establishes the sufficient and necessary relationship between the exact…
Many real world practical problems can be formulated as $\ell_{0}$-minimization problems with nonnegativity constraints, which seek the sparsest nonnegative signals to underdetermined linear systems. They have been widely applied in signal…
High-dimensional signal recovery of standard linear regression is a key challenge in many engineering fields, such as, communications, compressed sensing, and image processing. The approximate message passing (AMP) algorithm proposed by…
The theory behind compressive sampling pre-supposes that a given sequence of observations may be exactly represented by a linear combination of a small number of basis vectors. In practice, however, even small deviations from an exact…
We consider the compressed sensing problem, where the object $x_0 \in \bR^N$ is to be recovered from incomplete measurements $y = Ax_0 + z$; here the sensing matrix $A$ is an $n \times N$ random matrix with iid Gaussian entries and $n < N$.…
One-bit compressed sensing (1bCS) addresses the recovery of sparse signals from highly quantized measurements, retaining only the sign of each linear measurement. In the support recovery setting, the goal is to identify $\text{supp}(x)$,…