NDLI: Analysis of MMSE estimation for compressive sensing of block sparse signals

Content Provider	IEEE Xplore Digital Library
Author	Vehkapera, M. Chatterjee, S. Skoglund, M.
Copyright Year	2011
Description	Author affiliation: School of Electrical Engineering and the ACCESS Linnaeus Center KTH Royal Institute of Technology, SE-10044, Stockholm, Sweden (Vehkapera, M.; Chatterjee, S.; Skoglund, M.)
Abstract	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.
Starting Page	553
Ending Page	557
File Size	585477
Page Count	5
File Format	PDF
ISBN	9781457704383
e-ISBN	9781457704376
DOI	10.1109/ITW.2011.6089563
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-10-16
Publisher Place	Brazil
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Vectors Noise measurement Compressed sensing Noise Estimation Conferences Physics
Content Type	Text
Resource Type	Article

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