Related papers: The gap between the null space property and the re…
This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that properly constrained nuclear-norm…
This article considers the recovery of low-rank matrices via a convex nuclear-norm minimization problem and presents two null space properties (NSP) which characterize uniform recovery for the case of block-diagonal matrices and…
This paper studies the convergence of the adaptively iterative thresholding (AIT) algorithm for compressed sensing. We first introduce a generalized restricted isometry property (gRIP). Then we prove that the AIT algorithm converges to the…
A sufficient condition reported very recently for perfect recovery of a K-sparse vector via orthogonal matching pursuit (OMP) in K iterations is that the restricted isometry constant of the sensing matrix satisfies…
Under the assumption that a finite signal with different sampling lengths or different sampling frequencies is considered as equivalent, the signal space is considered as the quotient space of $\mathbb{R}^{\infty}$ over equivalence. The…
In this article we present a statistical version of the Candes-Tao restricted isometry property (SRIP for short) which holds in general for any incoherent dictionary which is a disjoint union of orthonormal bases. In addition, we show that,…
In this paper we theoretically study exact recovery of sparse vectors from compressed measurements by minimizing a general nonconvex function that can be decomposed into the sum of single variable functions belonging to a class of smooth…
We consider the problem of constructing a linear map from a Hilbert space $\mathcal{H}$ (possibly infinite dimensional) to $\mathbb{R}^m$ that satisfies a restricted isometry property (RIP) on an arbitrary signal model $\mathcal{S} \subset…
Recently, many works have focused on the characterization of non-linear dimensionality reduction methods obtained by quantizing linear embeddings, e.g., to reach fast processing time, efficient data compression procedures, novel…
Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy this…
Several exact recovery criteria (ERC) ensuring that orthogonal matching pursuit (OMP) identifies the correct support of sparse signals have been developed in the last few years. These ERC rely on the restricted isometry property (RIP), the…
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…
Compressed sensing is a signal processing technique whereby the limits imposed by the Shannon--Nyquist theorem can be exceeded provided certain conditions are imposed on the signal. Such conditions occur in many real-world scenarios, and…
This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…
Generalized Orthogonal Matching Pursuit (gOMP) is a natural extension of OMP algorithm where unlike OMP, it may select $N (\geq1)$ atoms in each iteration. In this paper, we demonstrate that gOMP can successfully reconstruct a $K$-sparse…
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…
In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to…
We study compressive sensing in the spatial domain to achieve target localization, specifically direction of arrival (DOA), using multiple-input multiple-output (MIMO) radar. A sparse localization framework is proposed for a MIMO array in…
Nonconvex matrix recovery is known to contain no spurious local minima under a restricted isometry property (RIP) with a sufficiently small RIP constant $\delta$. If $\delta$ is too large, however, then counterexamples containing spurious…
Indoor location-based services rely on the availability of sufficiently accurate positioning in indoor spaces. A popular approach to positioning relies on so-called radio maps that contain pairs of a vector of Wi-Fi signal strength…