Performance bounds on compressed sensing with poisson noise

Rebecca M. Willett, Maxim Raginsky

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

Abstract

This paper describes performance bounds for compressed sensing in the presence of Poisson noise when the underlying signal, a vector of Poisson intensities, is sparse or compressible (admits a sparse approximation). The signalindependent and bounded noise models used in the literature to analyze the performance of compressed sensing do not accurately model the effects of Poisson noise. However, Poisson noise is an appropriate noise model for a variety of applications, including low-light imaging, where sensing hardware is large or expensive, and limiting the number of measurements collected is important. In this paper, we describe how a feasible positivity-preserving sensing matrix can be constructed, and then analyze the performance of a compressed sensing reconstruction approach for Poisson data that minimizes an objective function consisting of a negative Poisson log likelihood term and a penalty term which could be used as a measure of signal sparsity.

Original languageEnglish (US)
Title of host publication2009 IEEE International Symposium on Information Theory, ISIT 2009
Pages174-178
Number of pages5
DOIs
StatePublished - Nov 19 2009
Externally publishedYes
Event2009 IEEE International Symposium on Information Theory, ISIT 2009 - Seoul, Korea, Republic of
Duration: Jun 28 2009Jul 3 2009

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8102

Other

Other2009 IEEE International Symposium on Information Theory, ISIT 2009
CountryKorea, Republic of
CitySeoul
Period6/28/097/3/09

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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  • Cite this

    Willett, R. M., & Raginsky, M. (2009). Performance bounds on compressed sensing with poisson noise. In 2009 IEEE International Symposium on Information Theory, ISIT 2009 (pp. 174-178). [5205258] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2009.5205258