Related papers: Support Recovery for Sparse Multidimensional Phase…
We consider the problem of exact support recovery of sparse signals via noisy measurements. The main focus is the sufficient and necessary conditions on the number of measurements for support recovery to be reliable. By drawing an analogy…
Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…
For the first time, this paper investigates the phase retrieval problem with the assumption that the phase (of the complex signal) is sparse in contrast to the sparsity assumption on the signal itself as considered in the literature of…
The support recovery problem consists of determining a sparse subset of variables that is relevant in generating a set of observations. In this paper, we study the support recovery problem in the phase retrieval model consisting of noisy…
We present a novel sparse signal reconstruction method "ISD", aiming to achieve fast reconstruction and a reduced requirement on the number of measurements compared to the classical l_1 minimization approach. ISD addresses failed…
A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given…
Support recovery of sparse signals from compressed linear measurements is a fundamental problem in compressed sensing (CS). In this paper, we study the orthogonal matching pursuit (OMP) algorithm for the recovery of support under noise. We…
Suppose we wish to recover a signal x in C^n from m intensity measurements of the form |<x,z_i>|^2, i = 1, 2,..., m; that is, from data in which phase information is missing. We prove that if the vectors z_i are sampled independently and…
We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. An uncertainty relation for block-sparse signals is derived, based on a block-coherence measure, which we…
The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a…
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…
In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…
We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of…
We study the problem of recovering the common $k$-sized support of a set of $n$ samples of dimension $d$, using $m$ noisy linear measurements per sample. Most prior work has focused on the case when $m$ exceeds $k$, in which case $n$ of the…
Lower dimensional signal representation schemes frequently assume that the signal of interest lies in a single vector space. In the context of the recently developed theory of compressive sensing (CS), it is often assumed that the signal of…
We address the problem of recovering a signal (up to global phase) from its short-time Fourier transform (STFT) magnitude measurements. This problem arises in several applications, including optical imaging and speech processing. In this…
The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The…
We propose robust and efficient algorithms for the joint sparse recovery problem in compressed sensing, which simultaneously recover the supports of jointly sparse signals from their multiple measurement vectors obtained through a common…
We study the support recovery problem for a high-dimensional signal observed with additive noise. With suitable parametrization of the signal sparsity and magnitude of its non-zero components, we characterize a phase-transition phenomenon…
In this paper, we study the missing sample recovery problem using methods based on sparse approximation. In this regard, we investigate the algorithms used for solving the inverse problem associated with the restoration of missed samples of…