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We study the recovery of sparse signals from underdetermined linear measurements when a potentially erroneous support estimate is available. Our results are twofold. First, we derive necessary and sufficient conditions for signal recovery…

Information Theory · Computer Science 2014-12-05 Hassan Mansour , Rayan Saab

The sparse signal recovery in the standard compressed sensing (CS) problem requires that the sensing matrix be known a priori. Such an ideal assumption may not be met in practical applications where various errors and fluctuations exist in…

Information Theory · Computer Science 2015-06-03 Zai Yang , Cishen Zhang , Lihua Xie

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…

Information Theory · Computer Science 2015-10-28 Jian Wang

This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements -- L_1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized…

Numerical Analysis · Mathematics 2008-03-15 Deanna Needell , Roman Vershynin

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…

Information Theory · Computer Science 2014-11-04 Holger Rauhut , Maryia Kabanava

Over the past years, there are increasing interests in recovering the signals from undersampling data where such signals are sparse under some orthogonal dictionary or tight framework, which is referred to be sparse synthetic model. More…

Information Theory · Computer Science 2012-02-10 Lianlin Li

The problem of multiple sensors simultaneously acquiring measurements of a single object can be found in many applications. In this paper, we present the optimal recovery guarantees for the recovery of compressible signals from multi-sensor…

Information Theory · Computer Science 2023-08-31 Il Yong Chun , Chen Li , Ben Adcock

We introduce and analyze a framework for function interpolation using compressed sensing. This framework - which is based on weighted $\ell^1$ minimization - does not require a priori bounds on the expansion tail in either its…

Numerical Analysis · Mathematics 2017-01-24 Ben Adcock

This paper introduces a novel approach for recovering sparse signals using sorted L1/L2 minimization. The proposed method assigns higher weights to indices with smaller absolute values and lower weights to larger values, effectively…

Numerical Analysis · Mathematics 2023-08-09 Chao Wang , Ming Yan , Junjie Yu

We consider the Orthogonal Least-Squares (OLS) algorithm for the recovery of a $m$-dimensional $k$-sparse signal from a low number of noisy linear measurements. The Exact Recovery Condition (ERC) in bounded noisy scenario is established for…

Machine Learning · Statistics 2016-08-09 Abolfazl Hashemi , Haris Vikalo

Infinite-dimensional compressed sensing deals with the recovery of analog signals (functions) from linear measurements, often in the form of integral transforms such as the Fourier transform. This framework is well-suited to many real-world…

Information Theory · Computer Science 2021-05-25 Ben Adcock , Vegard Antun , Anders C. Hansen

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…

Information Theory · Computer Science 2012-06-26 Galen Reeves , Michael Gastpar

Prior support constrained compressed sensing has of late become popular due to its potential for applications. The existing results on recovery guarantees provide global recovery bounds in the sense that they deal with full support.…

Optimization and Control · Mathematics 2020-07-03 K. Z. Najiya , Munnu Sonkar , C. S. Sastry

We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…

Information Theory · Computer Science 2020-10-20 Hendrik Bernd Petersen , Peter Jung

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…

Information Theory · Computer Science 2019-09-18 Jan-Hendrik Lange , Marc E. Pfetsch , Bianca M. Seib , Andreas M. Tillmann

Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…

Statistics Theory · Mathematics 2016-11-15 Henrik Ohlsson , Allen Y. Yang , Roy Dong , S. Shankar Sastry

This paper studies the problem of recovering a signal from one-bit compressed sensing measurements under a manifold model; that is, assuming that the signal lies on or near a manifold of low intrinsic dimension. We provide a convex recovery…

Information Theory · Computer Science 2020-07-24 Mark A. Iwen , Felix Krahmer , Sara Krause-Solberg , Johannes Maly

This article extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a…

Probability · Mathematics 2010-11-10 Holger Rauhut , Karin Schnass , Pierre Vandergheynst

In this paper a new result of recovery of sparse vectors from deterministic and noisy measurements by l1 minimization is given. The sparse vector is randomly chosen and follows a generic p-sparse model introduced by Candes and al. The main…

Optimization and Control · Mathematics 2012-12-04 Charles Dossal , Rémi Tesson

This paper addresses sparse signal reconstruction under various types of structural side constraints with applications in multi-antenna systems. Side constraints may result from prior information on the measurement system and the sparse…

Information Retrieval · Computer Science 2021-06-18 Khaled Ardah , Martin Haardt , Tianyi Liu , Frederic Matter , Marius Pesavento , Marc E. Pfetsch