Optimal recovery from compressive measurements via denoising-based approximate message passing

Christopher A. Metzler, Arian Maleki, Richard G. Baraniuk

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

6 Scopus citations

Abstract

Recently progress has been made in compressive sensing by replacing simplistic sparsity models with more powerful denoisers. In this paper, we develop a framework to predict the performance of denoising-based signal recovery algorithms based on a new deterministic state evolution formalism for approximate message passing. We compare our deterministic state evolution against its more classical Bayesian counterpart. We demonstrate that, while the two state evolutions are very similar, the deterministic framework is far more flexible. We apply the deterministic state evolution to explore the optimality of denoising-based approximate message passing (D-AMP). We prove that, while D-AMP is suboptimal for certain classes of signals, no algorithm can uniformly outperform it.

Original languageEnglish (US)
Title of host publication2015 International Conference on Sampling Theory and Applications, SampTA 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages508-512
Number of pages5
ISBN (Electronic)9781467373531
DOIs
StatePublished - Jul 2 2015
Event11th International Conference on Sampling Theory and Applications, SampTA 2015 - Washington, United States
Duration: May 25 2015May 29 2015

Publication series

Name2015 International Conference on Sampling Theory and Applications, SampTA 2015

Other

Other11th International Conference on Sampling Theory and Applications, SampTA 2015
CountryUnited States
CityWashington
Period5/25/155/29/15

Keywords

  • Approximate Message Passing
  • Compressed Sensing
  • Denoising
  • State Evolution

ASJC Scopus subject areas

  • Signal Processing
  • Statistics and Probability
  • Discrete Mathematics and Combinatorics

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