Sparse Signal Reconstruction for Overdispersed Low-photon Count Biomedical Imaging Using $\ell_p$ Total Variation
This work addresses image quality issues in medical imaging for healthcare applications, but it is incremental as it builds on existing regularization methods.
The paper tackles the problem of sparse signal reconstruction in low-photon biomedical imaging by using an ℓ_p total variation regularization within a negative binomial model, showing improved image reconstruction outcomes compared to Poisson models.
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.