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

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. ...

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

2011
*
2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
*

The problem

doi:10.1109/icassp.2011.5947237
dblp:conf/icassp/ShedthikereC11
fatcat:pdy3vdakbnburfdbqtjrhzryi4
*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. ...##
###
Information-Theoretic Limits on Sparse Signal Recovery: Dense versus Sparse Measurement Matrices

2010
*
IEEE Transactions on Information Theory
*

We study the information-theoretic limits

doi:10.1109/tit.2010.2046199
fatcat:juxxztaykzai5p7lxjulktv7di
*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. ...##
###
Model-based compressive sensing for multi-party distant speech recognition

2011
*
2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
*

We leverage the recent algorithmic advances in compressive sensing, and propose

doi:10.1109/icassp.2011.5947379
dblp:conf/icassp/AsaeiBC11
fatcat:gzadkg4t6jdthkwirfqdm2texa
*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 ...##
###
An Empirical-Bayes Approach to Recovering Linearly Constrained Non-Negative Sparse Signals

2014
*
IEEE Transactions on Signal Processing
*

We propose two novel approaches to the

doi:10.1109/tsp.2014.2337841
fatcat:yxrwi3hrfvfzdhfk4644zhu34m
*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 ...##
###
Sparse source separation from orthogonal mixtures

2009
*
2009 IEEE International Conference on Acoustics, Speech and Signal Processing
*

This paper addresses source separation

doi:10.1109/icassp.2009.4960291
dblp:conf/icassp/MishaliE09
fatcat:p3auzz6cmrcmvem3w7t5bhhjsi
*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. ...##
###
An empirical-bayes approach to recovering linearly constrained non-negative sparse signals

2013
*
2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)
*

We consider the

doi:10.1109/camsap.2013.6713993
dblp:conf/camsap/VilaS13
fatcat:td66wc7p35eynfxpc2kejrmu6i
*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 ...##
###
Distributed compressed sensing of Hyperspectral images via blind source separation

2010
*
2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers
*

In this work, we assume few number

doi:10.1109/acssc.2010.5757497
fatcat:jpyr2ubisrhh3akl725ygtab7e
*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*. ...##
###
Sparse Signal Recovery from a Mixture of Linear and Magnitude-Only Measurements

2015
*
IEEE Signal Processing Letters
*

We consider the problem

doi:10.1109/lsp.2015.2393295
pmid:29187781
pmcid:PMC5703438
fatcat:zatjlransfcuzezdb6s5qiap5e
*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. ...##
###
On Recovery of Sparse Signals in Compressed DNA Microarrays

2007
*
Asilomar Conference on Signals, Systems and Computers. Conference Record
*

To recover

doi:10.1109/acssc.2007.4487303
fatcat:6h4wulhrnbcjplbvmzdjparpoe
*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. ...##
###
Sparsity estimation from compressive projections via sparse random matrices

2018
*
EURASIP Journal on Advances in Signal Processing
*

The aim

doi:10.1186/s13634-018-0578-0
pmid:30956656
pmcid:PMC6414084
fatcat:oz45y6yikzhhxd6wdnyxdn24fu
*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. ...##
###
A Distributed Compressive Sensing Technique for Data Gathering in Wireless Sensor Networks

2013
*
Procedia Computer Science
*

The strength

doi:10.1016/j.procs.2013.09.028
fatcat:dzst6s6lbba45gmwplqlgpmdqe
*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. ...##
###
Interval-Passing Algorithm for Chemical Mixture Estimation

2013
*
IEEE Signal Processing Letters
*

We show that by applying an appropriate

doi:10.1109/lsp.2013.2267656
fatcat:46kamev6ffc7pcottktnkhglw4
*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. ...##
###
Information-theoretic limits on sparse support recovery: Dense versus sparse measurements

2008
*
2008 IEEE International Symposium on Information Theory
*

We study the information-theoretic limits

doi:10.1109/isit.2008.4595380
dblp:conf/isit/WangWR08
fatcat:ujvawejhjbcctmqs6emlagwcwu
*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. ...##
###
Information-theoretic limits on sparse signal recovery: Dense versus sparse measurement matrices
[article]

2008
*
arXiv
*
pre-print

We study the information-theoretic limits

arXiv:0806.0604v1
fatcat:kpb62qx6qrat5l4cjv2ki4uxvq
*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. ...
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