Performance bounds for expander-based compressed sensing in the presence of Poisson noise

Sina Jafarpour, Rebecca Willett, Maxim Raginsky, Robert Calderbank

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

Abstract

This paper provides performance bounds for compressed sensing in the presence of Poisson noise using expander graphs. The Poisson noise model is appropriate for a variety of applications, including low-light imaging and digital streaming, where the signal-independent and/or bounded noise models used in the compressed sensing literature are no longer applicable. In this paper, we develop a novel sensing paradigm based on expander graphs and propose a MAP algorithm for recovering sparse or compressible signals from Poisson observations. The geometry of the expander graphs and the positivity of the corresponding sensing matrices play a crucial role in establishing the bounds on the signal reconstruction error of the proposed algorithm. The geometry of the expander graphs makes them provably superior to random dense sensing matrices, such as Gaussian or partial Fourier ensembles, for the Poisson noise model.We support our results with experimental demonstrations.

Original languageEnglish (US)
Title of host publicationConference Record - 43rd Asilomar Conference on Signals, Systems and Computers
Pages513-517
Number of pages5
DOIs
StatePublished - Dec 1 2009
Externally publishedYes
Event43rd Asilomar Conference on Signals, Systems and Computers - Pacific Grove, CA, United States
Duration: Nov 1 2009Nov 4 2009

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
ISSN (Print)1058-6393

Other

Other43rd Asilomar Conference on Signals, Systems and Computers
CountryUnited States
CityPacific Grove, CA
Period11/1/0911/4/09

ASJC Scopus subject areas

  • Signal Processing
  • Computer Networks and Communications

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  • Cite this

    Jafarpour, S., Willett, R., Raginsky, M., & Calderbank, R. (2009). Performance bounds for expander-based compressed sensing in the presence of Poisson noise. In Conference Record - 43rd Asilomar Conference on Signals, Systems and Computers (pp. 513-517). [5469879] (Conference Record - Asilomar Conference on Signals, Systems and Computers). https://doi.org/10.1109/ACSSC.2009.5469879