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Analysis of MMSE estimation for compressive sensing of block sparse signals
KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0003-2638-6047
KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0002-7926-5081
2011 (English)In: 2011 IEEE Information Theory Workshop, ITW 2011, 2011, 553-557 p.Conference paper, Published paper (Refereed)
Abstract [en]

Minimum mean square error (MMSE) estimation of block sparse signals from noisy linear measurements is considered. Unlike in the standard compressive sensing setup where the non-zero entries of the signal are independently and uniformly distributed across the vector of interest, the information bearing components appear here in large mutually dependent clusters. Using the replica method from statistical physics, we derive a simple closed-form solution for the MMSE obtained by the optimum estimator. We show that the MMSE is a version of the Tse-Hanly formula with system load and MSE scaled by a parameter that depends on the sparsity pattern of the source. It turns out that this is equal to the MSE obtained by a genie-aided MMSE estimator which is informed in advance about the exact locations of the non-zero blocks. The asymptotic results obtained by the non-rigorous replica method are found to have an excellent agreement with finite sized numerical simulations.

Place, publisher, year, edition, pages
2011. 553-557 p.
Keyword [en]
Compressive sensing, sparsity, statistical mechanics
National Category
Telecommunications Signal Processing
Research subject
SRA - ICT
Identifiers
URN: urn:nbn:se:kth:diva-46535DOI: 10.1109/ITW.2011.6089563ISI: 000299416200114Scopus ID: 2-s2.0-83655202644ISBN: 978-145770437-6 (print)OAI: oai:DiVA.org:kth-46535DiVA: diva2:453876
Conference
2011 IEEE Information Theory Workshop, ITW 2011; Paraty; Brazil; 16 October 2011 through 20 October 2011
Funder
ICT - The Next Generation
Note

QC 20150707

Available from: 2011-11-03 Created: 2011-11-03 Last updated: 2015-07-07Bibliographically approved

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Chatterjee, SaikatSkoglund, Mikael

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