Generalized approximate message passing for cosparse analysis compressive sensing

Mark Borgerding, Philip Schniter, Jeremy Vila, Sundeep Rangan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In cosparse analysis compressive sensing (CS), one seeks to estimate a non-sparse signal vector from noisy sub-Nyquist linear measurements by exploiting the knowledge that a given linear transform of the signal is cosparse, i.e., has sufficiently many zeros. We propose a novel approach to cosparse analysis CS based on the generalized approximate message passing (GAMP) algorithm. Unlike other AMP-based approaches to this problem, ours works with a wide range of analysis operators and regularizers. In addition, we propose a novel ℓ0-like soft-thresholder based on MMSE denoising for a spike-and-slab distribution with an infinite-variance slab. Numerical demonstrations on synthetic and practical datasets demonstrate advantages over existing AMP-based, greedy, and reweighted-ℓ1 approaches.

Original languageEnglish (US)
Title of host publication2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3756-3760
Number of pages5
ISBN (Electronic)9781467369978
DOIs
StatePublished - Aug 4 2015
Event40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Brisbane, Australia
Duration: Apr 19 2014Apr 24 2014

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2015-August
ISSN (Print)1520-6149

Other

Other40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015
CountryAustralia
CityBrisbane
Period4/19/144/24/14

Keywords

  • Approximate message passing
  • belief propagation
  • compressed sensing

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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