Performance bounds for expander-based compressed sensing in poisson noise

Maxim Raginsky, Sina Jafarpour, Zachary T. Harmany, Roummel F. Marcia, Rebecca M. Willett, Robert Calderbank

Research output: Contribution to journalArticlepeer-review


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streaming, where the signal-independent and/or bounded noise models used in the compressed sensing literature are no longer applicable.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 maximum a posteriori (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. We support our results with experimental demonstrations of reconstructing average packet arrival rates and instantaneous packet counts at a router in a communication network, where the arrivals of packets in each flow follow a Poisson process.

Original languageEnglish (US)
Article number5776709
Pages (from-to)4139-4153
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number9
StatePublished - Sep 2011
Externally publishedYes


  • Compressive measurement
  • RIP-1
  • expander graphs
  • packet counters
  • photon-limited imaging

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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