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Model-based compressed sensing refers to compressed sensing with extra structure about the underlying sparse signal known a priori. Recent work has demonstrated that both for deterministic and probabilistic models imposed on the signal,…

Information Theory · Computer Science 2015-09-07 Sidhant Misra , Pablo A. Parrilo

We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occuring in clusters. Based on an uncertainty relation for block-sparse signals, we define a block-coherence measure and we show…

Information Theory · Computer Science 2008-12-02 Yonina C. Eldar , Helmut Bolcskei

In this paper, we propose a method for block sparse signal recovery that minimizes the block $q$-ratio sparsity $\left(\lVert z\rVert_{2,1}/\lVert z\rVert_{2,q}\right)^{\frac{q}{q-1}}$ with $q\in[0,\infty]$. For the case of $1<q\leq\infty$,…

Information Theory · Computer Science 2021-03-15 Zhiyong Zhou

In this paper, we consider the block-sparse signals recovery problem in the context of multiple measurement vectors (MMV) with common row sparsity patterns. We develop a new method for recovery of common row sparsity MMV signals, where a…

Machine Learning · Computer Science 2017-11-07 Hang Xiao , Zhengli Xing , Linxiao Yang , Jun Fang , Yanlun Wu

Compressive sensing predicts that sufficiently sparse vectors can be recovered from highly incomplete information. Efficient recovery methods such as $\ell_1$-minimization find the sparsest solution to certain systems of equations. Random…

Information Theory · Computer Science 2011-08-17 Ulaş Ayaz , Holger Rauhut

Deep neural network-based classifiers have been shown to be vulnerable to imperceptible perturbations to their input, such as $\ell_p$-bounded norm adversarial attacks. This has motivated the development of many defense methods, which are…

Machine Learning · Computer Science 2022-03-10 Darshan Thaker , Paris Giampouras , René Vidal

Block sparsity is an important parameter in many algorithms to successfully recover block sparse signals under the framework of compressive sensing. However, it is often unknown and needs to be estimated. Recently there emerges a few…

Signal Processing · Electrical Eng. & Systems 2019-09-04 Jianfeng Wang , Zhiyong Zhou , Jun Yu

In this paper we study recovery conditions of weighted $\ell_1$ minimization for signal reconstruction from compressed sensing measurements when partial support information is available. We show that if at least 50% of the (partial) support…

Information Theory · Computer Science 2011-07-26 Michael P. Friedlander , Hassan Mansour , Rayan Saab , Ozgur Yilmaz

In compressive sensing, sparse signals are recovered from underdetermined noisy linear observations. One of the interesting problems which attracted a lot of attention in recent times is the support recovery or sparsity pattern recovery…

Information Theory · Computer Science 2010-04-26 Subhojit Som , Lee C Potter

The problem of the distributed recovery of jointly sparse signals has attracted much attention recently. Let us assume that the nodes of a network observe different sparse signals with common support; starting from linear, compressed…

Optimization and Control · Mathematics 2016-11-15 Sophie M. Fosson , Javier Matamoros , Carles Anton-Haro , Enrico Magli

In the context of compressed sensing (CS), this paper considers the problem of reconstructing sparse signals with the aid of other given correlated sources as multiple side information. To address this problem, we theoretically study a…

Information Theory · Computer Science 2017-01-19 Huynh Van Luong , Jurgen Seiler , Andre Kaup , Soren Forchhammer , Nikos Deligiannis

In many linear regression problems, including ill-posed inverse problems in image restoration, the data exhibit some sparse structures that can be used to regularize the inversion. To this end, a classical path is to use $\ell_{12}$ block…

Signal Processing · Electrical Eng. & Systems 2021-10-25 Charles-Alban Deledalle , Nicolas Papadakis , Joseph Salmon , Samuel Vaiter

This work considers recovery of signals that are sparse over two bases. For instance, a signal might be sparse in both time and frequency, or a matrix can be low rank and sparse simultaneously. To facilitate recovery, we consider minimizing…

Information Theory · Computer Science 2012-02-17 Samet Oymak , Babak Hassibi

Compressed sensing is a theory which guarantees the exact recovery of sparse signals from a small number of linear projections. The sampling schemes suggested by current compressed sensing theories are often of little practical relevance…

Information Theory · Computer Science 2014-07-22 Jérémie Bigot , Claire Boyer , Pierre Weiss

We discuss a general notion of "sparsity structure" and associated recoveries of a sparse signal from its linear image of reduced dimension possibly corrupted with noise. Our approach allows for unified treatment of (a) the "usual sparsity"…

Optimization and Control · Mathematics 2016-11-26 Anatoli Juditsky , Fatma Kilinc Karzan , Arkadi Nemirovski

It is now well understood that $\ell_1$ minimization algorithm is able to recover sparse signals from incomplete measurements [2], [1], [3] and sharp recoverable sparsity thresholds have also been obtained for the $\ell_1$ minimization…

Probability · Mathematics 2009-04-07 Weiyu Xu , M. Amin Khajehnejad , Salman Avestimehr , Babak Hassibi

Traditional sampling theories consider the problem of reconstructing an unknown signal $x$ from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that $x$ lies in a known subspace.…

Cellular Automata and Lattice Gases · Physics 2009-03-30 Yonina C. Eldar , Moshe Mishali

This work is about recovering an analysis-sparse vector, i.e. sparse vector in some transform domain, from under-sampled measurements. In real-world applications, there often exist random analysis-sparse vectors whose distribution in the…

Information Theory · Computer Science 2022-12-29 Raziyeh Takbiri , Sajad Daei

In this effort, we propose a convex optimization approach based on weighted $\ell_1$-regularization for reconstructing objects of interest, such as signals or images, that are sparse or compressible in a wavelet basis. We recover the…

Image and Video Processing · Electrical Eng. & Systems 2019-09-17 Joseph Daws , Armenak Petrosyan , Hoang Tran , Clayton G. Webster

Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse…

Information Theory · Computer Science 2015-03-20 Meng Wang , Weiyu Xu , Enrique Mallada , Ao Tang