Related papers: Exact Recovery Conditions for Sparse Representatio…
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…
The aim of this paper is to build up the theoretical framework for the recovery of sparse signals from the magnitude of the measurement. We first investigate the minimal number of measurements for the success of the recovery of sparse…
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…
We formulate sparse support recovery as a salient set identification problem and use information-theoretic analyses to characterize the recovery performance and sample complexity. We consider a very general model where we are not restricted…
In this letter, we present a unified result for the stable recovery bound of Lq(0 < q < 1) optimization model in compressed sensing, which is a constrained Lq minimization problem aware of the noise in a linear system. Specifically, without…
This paper provides novel results for the recovery of signals from undersampled measurements based on analysis $\ell_1$-minimization, when the analysis operator is given by a frame. We both provide so-called uniform and nonuniform recovery…
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…
We consider the following k-sparse recovery problem: design an m x n matrix A, such that for any signal x, given Ax we can efficiently recover x' satisfying ||x-x'||_1 <= C min_{k-sparse} x"} ||x-x"||_1. It is known that there exist…
In compressive sensing, sparse signals are recovered from underdetermined noisy linear observations. One of the interesting problems which attracted a lot of attention in recent times is the support recovery or sparsity pattern recovery…
In this paper, we consider the recovery of block sparse signals, whose nonzero entries appear in blocks (or clusters) rather than spread arbitrarily throughout the signal, from incomplete linear measurement. A high order sufficient…
Compressed sensing shows that a sparse signal can stably be recovered from incomplete linear measurements. But, in practical applications, some signals have additional structure, where the nonzero elements arise in some blocks. We call such…
We consider the problem of estimating the support of a vector $\beta^* \in \mathbb{R}^{p}$ based on observations contaminated by noise. A significant body of work has studied behavior of $\ell_1$-relaxations when applied to measurement…
We study graph matching between two correlated networks in the almost fully seeded regime, where all but a vanishing fraction of vertex correspondences are revealed. Concretely, we consider the correlated stochastic block model and assume…
We consider stability and uniqueness in real phase retrieval problems over general input sets. Specifically, we assume the data consists of noisy quadratic measurements of an unknown input x in R^n that lies in a general set T and study…
We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear…
We consider a sparse high dimensional regression model where the goal is to recover a $k$-sparse unknown vector $\beta^*$ from $n$ noisy linear observations of the form $Y=X\beta^*+W \in \mathbb{R}^n$ where $X \in \mathbb{R}^{n \times p}$…
Recovering a low-complexity signal from its noisy observations by regularization methods is a cornerstone of inverse problems and compressed sensing. Stable recovery ensures that the original signal can be approximated linearly by optimal…
The Restricted Isometry Property (RIP) is a fundamental property of a matrix enabling sparse recovery. Informally, an m x n matrix satisfies RIP of order k in the l_p norm if ||Ax||_p \approx ||x||_p for any vector x that is k-sparse, i.e.,…
We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…
In this letter, we first construct a counter example to show that for any given positive integer $K\geq 2$ and for any $\frac{1}{\sqrt{K+1}}\leq t<1$, there always exist a $K-$sparse $\x$ and a matrix $\A$ with the restricted isometry…