Performance bounds for expander-based compressed sensing in poisson noise


Journal Article

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streaming, where the signal-independent and/or bounded noise models used in the compressed sensing literature are no longer applicable.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. © 2011 IEEE.

Full Text

Duke Authors

Cited Authors

  • Raginsky, M; Jafarpour, S; Harmany, ZT; Marcia, RF; Willett, RM; Calderbank, R

Published Date

  • September 1, 2011

Published In

Volume / Issue

  • 59 / 9

Start / End Page

  • 4139 - 4153

International Standard Serial Number (ISSN)

  • 1053-587X

Digital Object Identifier (DOI)

  • 10.1109/TSP.2011.2157913

Citation Source

  • Scopus