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
Volume2015-August
ISBN (Print)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

Other

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

Fingerprint

Message passing
Demonstrations

Keywords

  • Approximate message passing
  • belief propagation
  • compressed sensing

ASJC Scopus subject areas

  • Signal Processing
  • Software
  • Electrical and Electronic Engineering

Cite this

Borgerding, M., Schniter, P., Vila, J., & Rangan, S. (2015). Generalized approximate message passing for cosparse analysis compressive sensing. In 2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings (Vol. 2015-August, pp. 3756-3760). [7178673] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2015.7178673

Generalized approximate message passing for cosparse analysis compressive sensing. / Borgerding, Mark; Schniter, Philip; Vila, Jeremy; Rangan, Sundeep.

2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings. Vol. 2015-August Institute of Electrical and Electronics Engineers Inc., 2015. p. 3756-3760 7178673.

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

Borgerding, M, Schniter, P, Vila, J & Rangan, S 2015, Generalized approximate message passing for cosparse analysis compressive sensing. in 2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings. vol. 2015-August, 7178673, Institute of Electrical and Electronics Engineers Inc., pp. 3756-3760, 40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015, Brisbane, Australia, 4/19/14. https://doi.org/10.1109/ICASSP.2015.7178673
Borgerding M, Schniter P, Vila J, Rangan S. Generalized approximate message passing for cosparse analysis compressive sensing. In 2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings. Vol. 2015-August. Institute of Electrical and Electronics Engineers Inc. 2015. p. 3756-3760. 7178673 https://doi.org/10.1109/ICASSP.2015.7178673
Borgerding, Mark ; Schniter, Philip ; Vila, Jeremy ; Rangan, Sundeep. / Generalized approximate message passing for cosparse analysis compressive sensing. 2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings. Vol. 2015-August Institute of Electrical and Electronics Engineers Inc., 2015. pp. 3756-3760
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