Compressed sensing performance bounds under Poisson noise

Abstract--This paper describes performance bounds for compressed sensing (CS) where the underlying sparse or compressible (sparsely approximable) signal is a vector of nonnegative intensities whose measurements are corrupted by Poisson noise. In this setting, standard CS techniques cannot be applied directly for several reasons. First, the usual signal-independent and/or bounded noise models do not apply to Poisson noise, which is nonadditive and signal-dependent. Second, the CS matrices typically considered are not feasible in real optical systems because they do not adhere to important constraints, such as nonnegativity and photon flux preservation. Third, the typical `2 0`1 minimization leads to overfitting in the high-intensity regions and oversmoothing in the low-intensity areas. In this paper, we describe how a feasible positivity- and flux-preserving sensing matrix can be constructed, and then analyze the performance of a CS reconstruction approach for Poisson data that minimize...

• Type: Journal
• Year: 2010
• Where: TSP
• Authors: Maxim Raginsky, Rebecca Willett, Zachary T. Harmany, Roummel F. Marcia
• Keywords: Artificial Intelligence, CS Reconstruction Approach, Negative Poisson Log, Poisson Noise, TSP 2010