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Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…

Data Structures and Algorithms · Computer Science 2022-03-09 Jonathan A. Kelner , Jerry Li , Allen Liu , Aaron Sidford , Kevin Tian

This work investigates the problem of signal recovery from undersampled noisy sub-Gaussian measurements under the assumption of a synthesis-based sparsity model. Solving the $\ell^1$-synthesis basis pursuit allows for a simultaneous…

Information Theory · Computer Science 2020-04-16 Maximilian März , Claire Boyer , Jonas Kahn , Pierre Weiss

This paper is motivated by the reconstruction problem on the sparse stochastic block model. Mossel, et. al. proved that a reconstruction algorithm that recovers an optimal fraction of the communities in the symmetric, 2-community case. The…

Probability · Mathematics 2023-12-20 Byron Chin , Allan Sly

In high-dimensional linear regression, the goal pursued here is to estimate an unknown regression function using linear combinations of a suitable set of covariates. One of the key assumptions for the success of any statistical procedure in…

Statistics Theory · Mathematics 2015-03-13 Philippe Rigollet , Alexandre Tsybakov

Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an L1-minimization problem, and this method is accurate…

Numerical Analysis · Mathematics 2009-04-27 Deanna Needell

We address the sparse signal recovery problem in the context of multiple measurement vectors (MMV) when elements in each nonzero row of the solution matrix are temporally correlated. Existing algorithms do not consider such temporal…

Machine Learning · Statistics 2011-08-18 Zhilin Zhang , Bhaskar D. Rao

In this paper we study the reconstruction of binary sparse signals from partial random circulant measurements. We show that the reconstruction via the least-squares algorithm is as good as the reconstruction via the usually used program…

Information Theory · Computer Science 2020-06-29 Sandra Keiper

This paper introduces a nonconvex approach for sparse signal recovery, proposing a novel model termed the $\tau_2$-model, which utilizes the squared $\ell_1/\ell_2$ norms for this purpose. Our model offers an advancement over the $\ell_0$…

Optimization and Control · Mathematics 2024-09-02 Jianqing Jia , Ashley Prater-Bennette , Lixin Shen , Erin E. Tripp

This paper concerns the problem of 1-bit compressed sensing, where the goal is to estimate a sparse signal from a few of its binary measurements. We study a non-convex sparsity-constrained program and present a novel and concise analysis…

Machine Learning · Computer Science 2020-07-10 Jie Shen

For Gaussian sampling matrices, we provide bounds on the minimal number of measurements $m$ required to achieve robust weighted sparse recovery guarantees in terms of how well a given prior model for the sparsity support aligns with the…

Numerical Analysis · Mathematics 2016-05-04 Bubacarr Bah , Rachel Ward

We are motivated by problems that arise in a number of applications such as Online Marketing and explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…

Statistics Theory · Mathematics 2016-11-17 D. Motamedvaziri , M. H. Rohban , V. Saligrama

In this paper, we consider the problem of sparse signal detection based on partial support set estimation with compressive measurements in a distributed network. Multiple nodes in the network are assumed to observe sparse signals which…

Applications · Statistics 2016-08-10 Thakshila Wimalajeewa , Pramod K. Varshney

Signal reconstruction is a crucial aspect of compressive sensing. In weighted cases, there are two common types of weights. In order to establish a unified framework for handling various types of weights, the sparse function is introduced.…

Classical Analysis and ODEs · Mathematics 2024-10-10 Xiaotong Liu , Yiyu Liang

In this paper, we consider the recovery of the high-dimensional block-sparse signal from a compressed set of measurements, where the non-zero coefficients of the recovered signal occur in a small number of blocks. Adopting the idea of deep…

Signal Processing · Electrical Eng. & Systems 2021-11-19 Rong Fu , Vincent Monardo , Tianyao Huang , Yimin Liu

To strike a balance between energy efficiency and data quality control, this paper proposes a sensor censoring scheme for distributed sparse signal recovery via compressive-sensing based wireless sensor networks. In the proposed approach,…

Information Theory · Computer Science 2018-01-16 Jwo-Yuh Wu , Ming-Hsun Yang , Tsang-Yi Wang

Binary measurements arise naturally in a variety of statistical and engineering applications. They may be inherent to the problem---e.g., in determining the relationship between genetics and the presence or absence of a disease---or they…

Information Theory · Computer Science 2014-08-01 Richard Baraniuk , Simon Foucart , Deanna Needell , Yaniv Plan , Mary Wootters

We consider the problem of recovering sparse vectors from underdetermined linear measurements via $\ell_p$-constrained basis pursuit. Previous analyses of this problem based on generalized restricted isometry properties have suggested that…

Information Theory · Computer Science 2015-04-21 Sjoerd Dirksen , Guillaume Lecué , Holger Rauhut

In this paper, we present a novel Bayesian approach to recover simultaneously block sparse signals in the presence of outliers. The key advantage of our proposed method is the ability to handle non-stationary outliers, i.e. outliers which…

Computer Vision and Pattern Recognition · Computer Science 2016-05-12 Igor Fedorov , Ritwik Giri , Bhaskar D. Rao , Truong Q. Nguyen

Sparse linear regression with ill-conditioned Gaussian random designs is widely believed to exhibit a statistical/computational gap, but there is surprisingly little formal evidence for this belief, even in the form of examples that are…

Data Structures and Algorithms · Computer Science 2022-03-08 Jonathan A. Kelner , Frederic Koehler , Raghu Meka , Dhruv Rohatgi

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…

Information Theory · Computer Science 2013-02-06 Galen Reeves , Michael Gastpar