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We study the minimization problem of a non-convex sparsity promoting penalty function, the transformed $l_1$ (TL1), and its application in compressed sensing (CS). The TL1 penalty interpolates $l_0$ and $l_1$ norms through a nonnegative…

Information Theory · Computer Science 2018-01-15 Shuai Zhang , Jack Xin

We consider the problem of learning a graph modeling the statistical relations of the $d$ variables from a dataset with $n$ samples $X \in \mathbb{R}^{n \times d}$. Standard approaches amount to searching for a precision matrix $\Theta$…

Machine Learning · Statistics 2023-12-13 Titouan Vayer , Etienne Lasalle , Rémi Gribonval , Paulo Gonçalves

The performance of estimating the common support for jointly sparse signals based on their projections onto lower-dimensional space is analyzed. Support recovery is formulated as a multiple-hypothesis testing problem. Both upper and lower…

Information Theory · Computer Science 2009-11-05 Gongguo Tang , Arye Nehorai

Compressed Sensing aims to capture attributes of a sparse signal using very few measurements. Cand\`{e}s and Tao showed that sparse reconstruction is possible if the sensing matrix acts as a near isometry on all $\boldsymbol{k}$-sparse…

Information Theory · Computer Science 2009-10-18 Robert Calderbank , Stephen Howard , Sina Jafarpour

Motivated by applications such as sparse PCA, in this paper we present provably-accurate one-pass algorithms for the sparse approximation of the top eigenvectors of extremely massive matrices based on a single compact linear sketch. The…

Information Theory · Computer Science 2026-05-06 Edem Boahen , Simone Brugiapaglia , Hung-Hsu Chou , Mark Iwen , Felix Krahmer

We have developed an approximate signal recovery algorithm with low computational cost for compressed sensing on the basis of randomly constructed sparse measurement matrices. The law of large numbers and the central limit theorem suggest…

Information Theory · Computer Science 2011-02-21 Yoshiyuki Kabashima , Tadashi Wadayama

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

We study sparse recovery with structured random measurement matrices having independent, identically distributed, and uniformly bounded rows and with a nontrivial covariance structure. This class of matrices arises from random sampling of…

Information Theory · Computer Science 2020-05-15 Simone Brugiapaglia , Sjoerd Dirksen , Hans Christian Jung , Holger Rauhut

In this article, we address the problem of reducing the number of required samples for Spherical Near-Field Antenna Measurements (SNF) by using Compressed Sensing (CS). A condition to ensure the numerical performance of sparse recovery…

Information Theory · Computer Science 2023-02-10 Arya Bangun , Cosme Culotta-López

Recovery of sparse vectors and low-rank matrices from a small number of linear measurements is well-known to be possible under various model assumptions on the measurements. The key requirement on the measurement matrices is typically the…

Numerical Analysis · Mathematics 2021-09-23 Mark A. Iwen , Deanna Needell , Michael Perlmutter , Elizaveta Rebrova

The task of reconstructing a low rank matrix from incomplete linear measurements arises in areas such as machine learning, quantum state tomography and in the phase retrieval problem. In this note, we study the particular setup that the…

Information Theory · Computer Science 2016-12-12 Holger Rauhut , Ulrich Terstiege

This paper presents an adaptive and intelligent sparse model for digital image sampling and recovery. In the proposed sampler, we adaptively determine the number of required samples for retrieving image based on space-frequency-gradient…

Computer Vision and Pattern Recognition · Computer Science 2017-11-27 Ali Taimori , Farokh Marvasti

We consider algorithms and recovery guarantees for the analysis sparse model in which the signal is sparse with respect to a highly coherent frame. We consider the use of a monotone version of the fast iterative shrinkage- thresholding…

Optimization and Control · Mathematics 2015-06-17 Zhao Tan , Yonina C. Eldar , Amir Beck , Arye Nehorai

Sparse recovery principles play an important role in solving many nonlinear ill-posed inverse problems. We investigate a variational framework with support Oracle for compressed sensing sparse reconstructions, where the available…

Numerical Analysis · Mathematics 2024-04-10 Damiana Lazzaro , Serena Morigi , Luca Ratti

We investigate a power-constrained sensing matrix design problem for a compressed sensing framework. We adopt a mean square error (MSE) performance criterion for sparse source reconstruction in a system where the source-to-sensor channel…

Information Theory · Computer Science 2014-09-29 Amirpasha Shirazinia , Subhrakanti Dey

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…

Information Theory · Computer Science 2014-04-29 Holger Rauhut , Justin Romberg , Joel A. Tropp

Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…

Computational Physics · Physics 2013-02-04 Zai Yang , Cishen Zhang , Lihua Xie

Tremendous efforts have been made to study the theoretical and algorithmic aspects of sparse recovery and low-rank matrix recovery. This paper fills a theoretical gap in matrix recovery: the optimal sample complexity for stable recovery…

Information Theory · Computer Science 2017-12-27 Yanjun Li , Kiryung Lee , Yoram Bresler

Tremendous efforts have been made to study the theoretical and algorithmic aspects of sparse recovery and low-rank matrix recovery. This paper fills a theoretical gap in matrix recovery: the optimal sample complexity for stable recovery…

Information Theory · Computer Science 2018-01-03 Yanjun Li , Kiryung Lee , Yoram Bresler

In this paper, we consider the problem of compressed sensing where the goal is to recover almost all the sparse vectors using a small number of fixed linear measurements. For this problem, we propose a novel partial hard-thresholding…

Information Theory · Computer Science 2011-06-15 Prateek Jain , Ambuj Tewari , Inderjit S. Dhillon