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

• URL: http://arxiv.org/abs/2408.16622v1
• Date: Thu, 29 Aug 2024 15:31:43 GMT
• Title: Sparse Signal Reconstruction for Overdispersed Low-photon Count Biomedical Imaging Using $\ell_p$ Total Variation
• Authors: Yu Lu, Roummel F. Marcia,
• Abstract summary: We investigate 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.
• Score: 6.228193841473626
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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