Sparse Signal Reconstruction for Overdispersed Low-photon Count Biomedical Imaging Using $\ell_p$ Total Variation

TL;DR

This paper introduces a novel approach for low-photon count biomedical imaging that employs $ ext{ell}_p$ total variation regularization within a negative binomial model, improving image reconstruction in photon-limited scenarios.

Contribution

The study investigates $ ext{ell}_p$ TV quasi-seminorms in the negative binomial model for the first time, providing a gradient-based optimization method and comparative analysis with Poisson models.

Findings

Negative binomial model with $ ext{ell}_p$ TV improves reconstruction quality.

Proposed method outperforms traditional Poisson-based approaches.

Experimental results validate the effectiveness of the new regularization technique.

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 $\ell_p$ quasi-norm with $0 < p < 1$, $\ell_1$ 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 $\ell_p$ quasi-seminorm, both isotropic and anisotropic $\ell_p$ 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 $\ell_p$ TV quasi-seminorm as well as common penalty terms. Our experimental results highlight the efficacy of the proposed method.