Performance bounds for expander-based compressed sensing in Poisson noise

TL;DR

This paper establishes performance bounds for expander graph-based compressed sensing under Poisson noise, relevant for applications like low-light imaging and network traffic analysis, by developing a MAP recovery algorithm and analyzing its error bounds.

Contribution

It introduces a novel expander graph-based sensing paradigm and a MAP algorithm tailored for Poisson noise, with theoretical error bounds and practical demonstrations.

Findings

Performance bounds for Poisson noise compressed sensing are derived.

The proposed method effectively reconstructs signals in network traffic scenarios.

Experimental results validate the theoretical bounds and demonstrate practical utility.

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streaming, where the signal-independent and/or bounded noise models used in the compressed sensing literature are no longer applicable.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