Sparse Signal Reconstruction for Overdispersed Low-Photon Count Biomedical Imaging Using ℓp Total Variation

Yu Lu, Roummel F. Marcia

Abstract: The negative binomial model, which generalizes the Poisson distribution model, can be found in applications involving low-photon signal recovery, including medical imaging. Recent studies have explored several regularization terms for the negative binomial model, such as the ℓ p quasi-norm with 0 < p < 1, ℓ 1 norm, and the total variation (TV) quasi-seminorm for promoting sparsity in signal recovery. These penalty terms have been shown to improve image reconstruction outcomes. In this paper, we investigate the ℓ p quasi-seminorm, both isotropic and anisotropic ℓ p TV quasi-seminorms, within the framework of the negative binomial statistical model. This problem can be formulated as an optimization problem, which we solve using a gradient-based approach. We present comparisons between the negative binomial and Poisson statistical models using the ℓ p TV quasi-seminorm as well as common penalty terms. Our experimental results highlight the efficacy of the proposed method.