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There have been many matching pursuit algorithms (MPAs) which handle the sparse signal recovery problem a.k.a. compressed sensing (CS). In the MPAs, the correlation computation step has a dominant computational complexity. In this letter,…

Information Theory · Computer Science 2012-05-21 Kee-Hoon Kim , Hosung Park , Seokbeom Hong , Jong-Seon No , Habong Chung

A field known as Compressive Sensing (CS) has recently emerged to help address the growing challenges of capturing and processing high-dimensional signals and data sets. CS exploits the surprising fact that the information contained in a…

Machine Learning · Statistics 2010-02-08 Michael B. Wakin

Efficient algorithms for the sparse solution of under-determined linear systems $Ax = b$ are known for matrices $A$ satisfying suitable assumptions like the restricted isometry property (RIP). Without such assumptions little is known and…

Machine Learning · Computer Science 2021-01-22 G. Welper

We revisit the problem of computing with noisy information considered in Feige et al. 1994, which includes computing the OR function from noisy queries, and computing the MAX, SEARCH and SORT functions from noisy pairwise comparisons. For…

Data Structures and Algorithms · Computer Science 2023-06-22 Banghua Zhu , Ziao Wang , Nadim Ghaddar , Jiantao Jiao , Lele Wang

In this paper, compressed sensing with noisy measurements is addressed. The theoretically optimal reconstruction error is studied by evaluating Tanaka's equation. The main contribution is to show that in several regions, which have…

Information Theory · Computer Science 2013-02-19 Junan Zhu , Dror Baron

We consider compressed sampling over finite fields and investigate the number of compressed measurements needed for successful L0 recovery. Our results are obtained while the sparseness of the sensing matrices as well as the size of the…

Information Theory · Computer Science 2012-11-26 Jin-Taek Seong , Heung-No Lee

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

Quantization of compressed sensing measurements is typically justified by the robust recovery results of Cand\`es, Romberg and Tao, and of Donoho. These results guarantee that if a uniform quantizer of step size $\delta$ is used to quantize…

Information Theory · Computer Science 2010-10-06 S. Güntürk , A. Powell , R. Saab , Ö. Yılmaz

In this paper we look at a well known linear inverse problem that is one of the mathematical cornerstones of the compressed sensing field. In seminal works \cite{CRT,DOnoho06CS} $\ell_1$ optimization and its success when used for recovering…

Information Theory · Computer Science 2015-07-17 Mihailo Stojnic

We study the Compressed Sensing (CS) problem, which is the problem of finding the most sparse vector that satisfies a set of linear measurements up to some numerical tolerance. We introduce an $\ell_2$ regularized formulation of CS which we…

Signal Processing · Electrical Eng. & Systems 2024-07-15 Dimitris Bertsimas , Nicholas A. G. Johnson

Suppose that the collection $\{e_i\}_{i=1}^m$ forms a frame for $\R^k$, where each entry of the vector $e_i$ is a sub-Gaussian random variable. We consider expansions in such a frame, which are then quantized using a Sigma-Delta scheme. We…

Information Theory · Computer Science 2013-06-20 Felix Krahmer , Rayan Saab , Özgür Yılmaz

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

The problem of identifying sparse solutions for the link structure and dynamics of an unknown linear, time-invariant network is posed as finding sparse solutions x to Ax=b. If the sensing matrix A satisfies a rank condition, this problem…

Dynamical Systems · Mathematics 2014-11-18 David Hayden , Young Hwan Chang , Jorge Goncalves , Claire Tomlin

We consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The…

Information Theory · Computer Science 2020-10-15 Giovanni S. Alberti , Matteo Santacesaria

In this paper, designs and analyses of compressive recognition systems are discussed, and also a method of establishing a dual connection between designs of good communication codes and designs of recognition systems is presented. Pattern…

Information Theory · Computer Science 2007-12-24 Po-Hsiang Lai , Joseph A. O'Sullivan

Traditional compressed sensing considers sampling a 1D signal. For a multidimensional signal, if reshaped into a vector, the required size of the sensing matrix becomes dramatically large, which increases the storage and computational…

Information Theory · Computer Science 2016-11-17 Hao Fang , Sergiy A. Vorobyov , Hai Jiang , Omid Taheri

We consider the compressive sensing of a sparse or compressible signal ${\bf x} \in {\mathbb R}^M$. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce…

Information Theory · Computer Science 2009-03-05 Mehmet Akçakaya , Jinsoo Park , Vahid Tarokh

Noiseless compressive sensing is a protocol that enables undersampling and later recovery of a signal without loss of information. This compression is possible because the signal is usually sufficiently sparse in a given basis. Currently,…

Information Theory · Computer Science 2024-07-22 D. Barbier , C Lucibello , L. Saglietti , F. Krzakala , L. Zdeborova

The prohibitive sizes of Large Language Models (LLMs) today make it difficult to deploy them on memory-constrained edge devices. This work introduces $\rm CALDERA$ -- a new post-training LLM compression algorithm that harnesses the inherent…

Machine Learning · Computer Science 2024-11-05 Rajarshi Saha , Naomi Sagan , Varun Srivastava , Andrea J. Goldsmith , Mert Pilanci

One important problem in genome science is to determine sets of co-regulated genes based on measurements of gene expression levels across samples, where the quantification of expression levels includes substantial technical and biological…

Applications · Statistics 2013-10-18 Chuan Gao , Christopher D Brown , Barbara E Engelhardt