SPIRAL out of convexity: sparsityregularized algorithms for photonlimited imaging
Abstract
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 l_{2}l_{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 loglikelihood 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 approach incorporates key ideas of using quadratic separable approximations to the objective function at each iteration and computationally efficient partitionbased multiscale estimation methods.
 Publication:

Computational Imaging VIII
 Pub Date:
 January 2010
 DOI:
 10.1117/12.850771
 Bibcode:
 2010SPIE.7533E..0RH