Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 59, Issue 9, Pages 4139-4153Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2011.2157913
Keywords
Compressive measurement; expander graphs; packet counters; photon-limited imaging; RIP-1
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Funding
- NSF [CCF-06-43947, DMS-08-11062, DMS 0914892]
- DARPA [HR0011-07-1-003]
- ONR [N00014-08-1-1110]
- AFOSR [FA9550-09-1-0551]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0965711] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0914892] Funding Source: National Science Foundation
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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streaming, where the signal-independent and/or bounded noise models used in the compressed sensing literature are no longer applicable.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.
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