Overdispersed Photon-Limited Sparse Signal Recovery Using Nonconvex Regularization

Yu Lu, Roummel F. Marcia

Abstract: This paper investigates the application of the $\ell_{p}$ quasi-norm, where $0 < p < 1$ , in contexts characterized by photon-limited signals such as medical imaging and night vision. In these environments, low-photon count images have typically been modeled using Poisson statistics. In related algorithms, the $\ell_{1}$ norm is commonly employed as a regularization method to promotes sparsity in the reconstruction. However, recent research suggests that using the $\ell_{p}$ quasi-norm may yield lower error results. In this paper, we investigate the use of negative binomial statistics, which are more general models than Poisson models, in conjunction with the $\ell_{p}$ quasi-norm for recovering sparse signals in low-photon count imaging settings.