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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 the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed…

Statistics Theory · Mathematics 2019-10-23 Mohamed Ndaoud , Alexandre B. Tsybakov

Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…

Numerical Analysis · Mathematics 2018-01-08 Lenny Fukshansky , Deanna Needell , Benny Sudakov

We study the problem of jointly sparse support recovery with 1-bit compressive measurements in a sensor network. Sensors are assumed to observe sparse signals having the same but unknown sparse support. Each sensor quantizes its measurement…

Information Theory · Computer Science 2015-06-02 Vipul Gupta , Bhavya Kailkhura , Thakshila Wimalajeewa , Pramod K. Varshney

We observe an unknown regression function of $d$ variables $f(\boldsymbol{t})$, $\boldsymbol{t} \in[0,1]^d$, in the Gaussian white noise model of intensity $\varepsilon>0$. We assume that the function $f$ is regular and that it is a sum of…

Statistics Theory · Mathematics 2025-07-03 Natalia Stepanova , Marie Turcicova

We consider the problem of estimating an unknown coordinate-wise monotone function given noisy measurements, known as the isotonic regression problem. Often, only a small subset of the features affects the output. This motivates the sparse…

Statistics Theory · Mathematics 2019-07-04 David Gamarnik , Julia Gaudio

In compressed sensing, a small number of linear measurements can be used to reconstruct an unknown signal. Existing approaches leverage assumptions on the structure of these signals, such as sparsity or the availability of a generative…

Machine Learning · Statistics 2018-08-02 Manik Dhar , Aditya Grover , Stefano Ermon

During the last decade, the paradigm of compressed sensing has gained significant importance in the signal processing community. While the original idea was to utilize sparsity assumptions to design powerful recovery algorithms of vectors…

Functional Analysis · Mathematics 2016-07-07 Axel Flinth

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

One-bit compressive sensing has extended the scope of sparse recovery by showing that sparse signals can be accurately reconstructed even when their linear measurements are subject to the extreme quantization scenario of binary…

Information Theory · Computer Science 2016-06-27 Rich Baraniuk , Simon Foucart , Deanna Needell , Yaniv Plan , Mary Wootters

This paper addresses the problem of sparse recovery with graph constraints in the sense that we can take additive measurements over nodes only if they induce a connected subgraph. We provide explicit measurement constructions for several…

Information Theory · Computer Science 2011-08-03 Meng Wang , Weiyu Xu , Enrique Mallada , Ao Tang

In this paper, we analyze the information theoretic lower bound on the necessary number of samples needed for recovering a sparse signal under different compressed sensing settings. We focus on the weighted graph model, a model-based…

Information Theory · Computer Science 2022-09-16 Adarsh Barik , Jean Honorio

In this paper, we estimate the high dimensional precision matrix under the weak sparsity condition where many entries are nearly zero. We revisit the sparse column-wise inverse operator (SCIO) estimator \cite{liu2015fast} and derive its…

Statistics Theory · Mathematics 2022-10-21 Zeyu Wu , Cheng Wang , Weidong Liu

We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…

Information Theory · Computer Science 2015-06-17 Jeremy Vila , Philip Schniter

We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. An uncertainty relation for block-sparse signals is derived, based on a block-coherence measure, which we…

Information Theory · Computer Science 2015-05-13 Yonina C. Eldar , Patrick Kuppinger , Helmut Bölcskei

Recovering an unknown but structured signal from its measurements is a challenging problem with significant applications in fields such as imaging restoration, wireless communications, and signal processing. In this paper, we consider the…

Information Theory · Computer Science 2026-01-09 Yijun Zhong , Yi Shen

We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…

Information Theory · Computer Science 2013-11-12 Kishore Jaganathan , Samet Oymak , Babak Hassibi

In this paper we present a new algorithm for compressive sensing that makes use of binary measurement matrices and achieves exact recovery of ultra sparse vectors, in a single pass and without any iterations. Due to its noniterative nature,…

Information Theory · Computer Science 2018-05-22 Mahsa Lotfi , Mathukumalli Vidyasagar

Vector valued data appearing in concrete applications often possess sparse expansions with respect to a preassigned frame for each vector component individually. Additionally, different components may also exhibit common sparsity patterns.…

Numerical Analysis · Mathematics 2007-05-23 Massimo Fornasier , Holger Rauhut

We consider multichannel sparse recovery problem where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known…

Information Theory · Computer Science 2015-06-11 Esa Ollila