SPIRAL out of convexity: sparsity-regularized algorithms for photon-limited imaging

The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or temporally distributed phenomenon (f ) from Poisson data (y) cannot be accomplished by minimizing a conventional 2- 1 objective function. The problem addressed in this paper is the estimation of f from y in an inverse problem setting, where (a) the number of unknowns may potentially be larger than the number of observations and (b) f admits a sparse representation. The optimization formulation considered in this paper uses a negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). This paper describes computational methods for solving the constrained sparse Poisson inverse problem. In particular, the proposed appro...

• Type: Conference
• Year: 2010
• Where: CIMAGING
• Authors: Zachary T. Harmany, Roummel F. Marcia, Rebecca Willett
• Keywords: CIMAGING 2010, Hardware, Objective Function, Poisson, Poisson Noise Model