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We study the compressed sensing (CS) signal estimation problem where an input signal is measured via a linear matrix multiplication under additive noise. While this setup usually assumes sparsity or compressibility in the input signal…

Information Theory · Computer Science 2014-12-23 Junan Zhu , Dror Baron , Marco F. Duarte

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…

Information Theory · Computer Science 2015-06-12 Siddhartha Satpathi , Rajib Lochan Das , Mrityunjoy Chakraborty

Compressed sensing is a technique for recovering a high-dimensional signal from lower-dimensional data, whose components represent partial information about the signal, utilizing prior knowledge on the sparsity of the signal. For further…

Information Theory · Computer Science 2014-02-18 Yingying Xu , Yoshiyuki Kabashima

We study compressed sensing (CS) signal reconstruction problems where an input signal is measured via matrix multiplication under additive white Gaussian noise. Our signals are assumed to be stationary and ergodic, but the input statistics…

Information Theory · Computer Science 2014-10-22 Yanting Ma , Junan Zhu , Dror Baron

Dimensionality reduction is a popular approach to tackle high-dimensional data with low-dimensional nature. Subspace Restricted Isometry Property, a newly-proposed concept, has proved to be a useful tool in analyzing the effect of…

Information Theory · Computer Science 2019-10-01 Xingyu Xv , Gen Li , Yuantao Gu

Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase…

Optimization and Control · Mathematics 2016-12-30 Mateo Díaz , Mauricio Junca , Felipe Rincón , Mauricio Velasco

Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…

Information Theory · Computer Science 2015-07-03 Yipeng Liu

Compressed sensing seeks to invert an underdetermined linear system by exploiting additional knowledge of the true solution. Over the last decade, several instances of compressed sensing have been studied for various applications, and for…

Information Theory · Computer Science 2014-08-20 Jameson Cahill , Dustin G. Mixon

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…

Optimization and Control · Mathematics 2015-12-17 Yu Wang , Jinshan Zeng , Zhimin Peng , Xiangyu Chang , Zongben Xu

Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding…

Information Theory · Computer Science 2008-05-06 Thomas Blumensath , Mike E. Davies

We examine the problem of selecting a small set of linear measurements for reconstructing high-dimensional signals. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component…

Computer Vision and Pattern Recognition · Computer Science 2025-08-06 Ling-Qi Zhang , Zahra Kadkhodaie , Eero P. Simoncelli , David H. Brainard

In this paper, we study a general low-rank matrix recovery problem with linear measurements corrupted by some noise. The objective is to understand under what conditions on the restricted isometry property (RIP) of the problem local search…

Optimization and Control · Mathematics 2023-07-26 Ziye Ma , Yingjie Bi , Javad Lavaei , Somayeh Sojoudi

In colocated multiple-input multiple-output (MIMO) radar using compressive sensing (CS), a receive node compresses its received signal via a linear transformation, referred to as measurement matrix. The samples are subsequently forwarded to…

Information Theory · Computer Science 2015-05-27 Y. Yu , A. P. Petropulu , H. V. Poor

This paper describes performance bounds for compressed sensing (CS) where the underlying sparse or compressible (sparsely approximable) signal is a vector of nonnegative intensities whose measurements are corrupted by Poisson noise. In this…

Information Theory · Computer Science 2015-05-14 Maxim Raginsky , Rebecca M. Willett , Zachary T. Harmany , Roummel F. Marcia

The convergence of the generalized alternating projection (GAP) algorithm is studied in this paper to solve the compressive sensing problem $\yv = \Amat \xv + \epsilonv$. By assuming that $\Amat\Amat\ts$ is invertible, we prove that GAP…

Information Theory · Computer Science 2015-09-22 Xin Yuan , Hong Jiang , Paul Wilford

This work is concerned with the problem of recovering high-dimensional signals $\mathbf{x} \in \mathbb{R}^n$ which belong to a convex set of low-complexity from a small number of quantized measurements. We propose to estimate the signals…

Information Theory · Computer Science 2021-03-29 Hans Christian Jung , Johannes Maly , Lars Palzer , Alexander Stollenwerk

We study the problem of approximately recovering signals on a manifold from one-bit linear measurements drawn from either a Gaussian ensemble, partial circulant ensemble, or bounded orthonormal ensemble and quantized using Sigma-Delta or…

Information Theory · Computer Science 2019-04-25 Mark Iwen , Eric Lybrand , Aaron Nelson , Rayan Saab

We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…

Signal Processing · Electrical Eng. & Systems 2021-10-15 Michael Koller , Wolfgang Utschick

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…

Information Theory · Computer Science 2014-01-06 Ling-Hua Chang , Jwo-Yuh Wu

This paper follows the recent discussion on the sparse solution recovery with quasi-norms $\ell_q,~q\in(0,1)$ when the sensing matrix possesses a Restricted Isometry Constant $\delta_{2k}$ (RIC). Our key tool is an improvement on a version…

Information Theory · Computer Science 2013-12-13 Yong Hsia , Ruey-Lin Sheu