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Support Recovery of Sparse Signals from a Mixture of Linear Measurements [article]

Venkata Gandikota, Arya Mazumdar, Soumyabrata Pal
2021 arXiv   pre-print
Recovery of support of a sparse vector from simple measurements is a widely-studied problem, considered under the frameworks of compressed sensing, 1-bit compressed sensing, and more general single index  ...  We consider generalizations of this problem: mixtures of linear regressions, and mixtures of linear classifiers, where the goal is to recover supports of multiple sparse vectors using only a small number  ...  This work is supported in part by NSF awards 2133484, 2127929, and 1934846.  ... 
arXiv:2106.05951v2 fatcat:zaz4es42frhixk3vfhatmfxfby

Bayesian framework and message passing for joint support and signal recovery of approximately sparse signals

Shubha Shedthikere, A. Chockalingam
2011 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
The problem of recovery of strictly sparse signals from noisy measurements can be viewed as a problem of recovery of approximately sparse signals from noiseless measurements, making the approach applicable  ...  to strictly sparse signal recovery from noisy measurements.  ...  Fig. 4 . 4 % success versus L performance of support recovery of strictly sparse signals with noisy measurements for MMV.  ... 
doi:10.1109/icassp.2011.5947237 dblp:conf/icassp/ShedthikereC11 fatcat:pdy3vdakbnburfdbqtjrhzryi4

Information-Theoretic Limits on Sparse Signal Recovery: Dense versus Sparse Measurement Matrices

Wei Wang, Martin J. Wainwright, Kannan Ramchandran
2010 IEEE Transactions on Information Theory  
We study the information-theoretic limits of exactly recovering the support set of a sparse signal, using noisy projections defined by various classes of measurement matrices.  ...  size n, including the important special case of linear sparsity (k = 2(p)) using a linear scaling of observations (n = 2(p)).  ...  ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for helpful comments that improved the presentation of this paper.  ... 
doi:10.1109/tit.2010.2046199 fatcat:juxxztaykzai5p7lxjulktv7di

Model-based compressive sensing for multi-party distant speech recognition

Afsaneh Asaei, Herve Bourlard, Volkan Cevher
2011 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
We leverage the recent algorithmic advances in compressive sensing, and propose a novel source separation algorithm for efficient recovery of convolutive speech mixtures in spectro-temporal domain.  ...  Our results provide compelling evidence of the effectiveness of sparse recovery formulations in speech recognition.  ...  A new paradigm in CS exploits the inter-dependency structure underlying the support of the sparse coefficients in recovery algorithms to reduce the number of required measurements and to better differentiate  ... 
doi:10.1109/icassp.2011.5947379 dblp:conf/icassp/AsaeiBC11 fatcat:gzadkg4t6jdthkwirfqdm2texa

An Empirical-Bayes Approach to Recovering Linearly Constrained Non-Negative Sparse Signals

Jeremy P. Vila, Philip Schniter
2014 IEEE Transactions on Signal Processing  
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  ...  Our second approach is based on the sum-product version of the GAMP algorithm, where we propose the use of a Bernoulli non-negative Gaussian-mixture signal prior and a Laplacian likelihood, and propose  ...  INTRODUCTION We consider the recovery of an (approximately) sparse signal x ∈ R N from the noisy linear measurements y = Ax + w ∈ R M , (1) where A is a known sensing matrix, w is additive white Gaussian  ... 
doi:10.1109/tsp.2014.2337841 fatcat:yxrwi3hrfvfzdhfk4644zhu34m

Sparse source separation from orthogonal mixtures

Moshe Mishali, Yonina C. Eldar
2009 2009 IEEE International Conference on Acoustics, Speech and Signal Processing  
This paper addresses source separation from a linear mixture under two assumptions: source sparsity and orthogonality of the mixing matrix.  ...  In the second stage, the support is used to reformulate the recovery task as an optimization problem. We then suggest a solution based on alternating minimization.  ...  INTRODUCTION Blind source separation (BSS) is a fundamental problem in data analysis where the goal is to recover a set of source signals from their linear mixture, typically in the presence of noise.  ... 
doi:10.1109/icassp.2009.4960291 dblp:conf/icassp/MishaliE09 fatcat:p3auzz6cmrcmvem3w7t5bhhjsi

An empirical-bayes approach to recovering linearly constrained non-negative sparse signals

Jeremy Vila, Philip Schniter
2013 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)  
We consider the recovery of an (approximately) sparse signal from noisy linear measurements, in the case that the signal is apriori known to be non-negative and obeys certain linear equality constraints  ...  To enforce both sparsity and nonnegativity, we employ an i.i.d Bernoulli non-negative Gaussian mixture (NNGM) prior and perform approximate minimum mean-squared error (MMSE) recovery of the signal using  ...  INTRODUCTION We consider the recovery of an (approximately) sparse signal x ∈ R N from the noisy linear measurements y = Ax + w ∈ R M , (1) where A is a known sensing matrix, w is additive white Gaussian  ... 
doi:10.1109/camsap.2013.6713993 dblp:conf/camsap/VilaS13 fatcat:td66wc7p35eynfxpc2kejrmu6i

Distributed compressed sensing of Hyperspectral images via blind source separation

Mohammad Golbabaee, Simon Arberet, Pierre Vandergheynst
2010 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers  
In this work, we assume few number of sources are generating the multichannel observations based on a linear mixture model.  ...  algorithm to estimate both the sources and the mixing matrix (and thus the whole data) from the compressed measurements.  ...  Unlike the other methods for multichannel CS, our scheme attempts to improve recovery by exploiting dependencies across the channels via assuming a linear source mixture model for the signals.  ... 
doi:10.1109/acssc.2010.5757497 fatcat:jpyr2ubisrhh3akl725ygtab7e

Sparse Signal Recovery from a Mixture of Linear and Magnitude-Only Measurements

Mehmet Akcakaya, Vahid Tarokh
2015 IEEE Signal Processing Letters  
We consider the problem of exact sparse signal recovery from a combination of linear and magnitude-only (phaseless) measurements.  ...  We show that if max(2m 1 , 1) + m 2 ≥ 4k − 1, then a set of generic measurements are sufficient to recover every k-sparse x exactly, establishing the trade-off between the number of linear and magnitude-only  ...  Akçakaya would like to acknowledge grant support from NIH K99HL111410-01.  ... 
doi:10.1109/lsp.2015.2393295 pmid:29187781 pmcid:PMC5703438 fatcat:zatjlransfcuzezdb6s5qiap5e

On Recovery of Sparse Signals in Compressed DNA Microarrays

H. Vikalo, F. Parvaresh, B. Hassibi
2007 Asilomar Conference on Signals, Systems and Computers. Conference Record  
To recover signals from compressed microarray measurements, we leverage ideas from compressive sampling. Experimental verification of the proposed methodology is presented.  ...  This is a wasteful use of the sensing resources in comparative DNA microarray experiments, where a test sample is measured relative to a reference sample.  ...  In particular, recall that a sparse signal may be recovered from a small number of linear combinations of its components.  ... 
doi:10.1109/acssc.2007.4487303 fatcat:6h4wulhrnbcjplbvmzdjparpoe

Sparsity estimation from compressive projections via sparse random matrices

Chiara Ravazzi, Sophie Fosson, Tiziano Bianchi, Enrico Magli
2018 EURASIP Journal on Advances in Signal Processing  
The aim of this paper is to develop strategies to estimate the sparsity degree of a signal from compressive projections, without the burden of recovery.  ...  The proposed method employs γ-sparsified random matrices and is based on a maximum likelihood (ML) approach, exploiting the property that the acquired measurements are distributed according to a mixture  ...  Acknowledgments The authors thank the European Research Council for the financial support for this research.  ... 
doi:10.1186/s13634-018-0578-0 pmid:30956656 pmcid:PMC6414084 fatcat:oz45y6yikzhhxd6wdnyxdn24fu

A Distributed Compressive Sensing Technique for Data Gathering in Wireless Sensor Networks

Alireza Masoum, Nirvana Meratnia, Paul J.M. Havinga
2013 Procedia Computer Science  
The strength of compressive sensing is its ability to reconstruct sparse or compressible signals from small number of measurements without requiring any a priori knowledge about the signal structure.  ...  Our approach employs Bayesian inference to build probabilistic model of the signals and thereafter applies belief propagation algorithm as a decoding method to recover the common sparse signal.  ...  Compressive sensing theory states that if signal is K-sparse on basis, it can be captured and recovered from M nonadaptive, linear measurements ( ) with a certain restriction.  ... 
doi:10.1016/j.procs.2013.09.028 fatcat:dzst6s6lbba45gmwplqlgpmdqe

Interval-Passing Algorithm for Chemical Mixture Estimation

L. Danjean, B. Vasic, M. W. Marcellin, D. Declercq
2013 IEEE Signal Processing Letters  
We show that by applying an appropriate measurement matrix on the chemical mixture spectrum, we obtain an overall measurement matrix which is sparse.  ...  Simulation results for the proportion of correct reconstructions show that chemical mixtures with a large number of chemicals present can be recovered.  ...  Instead of using a measurement matrix M which is sparse, the AMP requires M to be a random matrix whose elements are i.i.d. drawn from some distribution, taken here to be Gaussian.  ... 
doi:10.1109/lsp.2013.2267656 fatcat:46kamev6ffc7pcottktnkhglw4

Information-theoretic limits on sparse support recovery: Dense versus sparse measurements

Wei Wang, Martin J. Wainwright, Kannan Ramchandran
2008 2008 IEEE International Symposium on Information Theory  
We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices.  ...  We derive lower bounds on the number of observations required for exact sparsity recovery, as a function of the signal dimension p, signal sparsity k, and measurement sparsity γ.  ...  Acknowledgment The work of WW and KR was supported by NSF grant CCF-0635114. The work of MJW was supported by NSF grants CAREER-CCF-0545862 and DMS-0605165.  ... 
doi:10.1109/isit.2008.4595380 dblp:conf/isit/WangWR08 fatcat:ujvawejhjbcctmqs6emlagwcwu

Information-theoretic limits on sparse signal recovery: Dense versus sparse measurement matrices [article]

Wei Wang, Martin J. Wainwright, Kannan Ramchandran
2008 arXiv   pre-print
We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices.  ...  n, including the important special case of linear sparsity (k = Θ(p)) using a linear scaling of observations (n = Θ(p)).  ...  Acknowledgment The work of WW and KR was supported by NSF grant CCF-0635114. The work of MJW was supported by NSF grants CAREER-CCF-0545862 and DMS-0605165.  ... 
arXiv:0806.0604v1 fatcat:kpb62qx6qrat5l4cjv2ki4uxvq
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