Sparse Signal Reconstruction for Overdispersed Low-photon Count Biomedical Imaging Using $\ell_p$ Total Variation
<|reference_start|>Sparse Signal Reconstruction for Overdispersed Low-photon Count Biomedical Imaging Using $\ell_p$ Total Variation: 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.<|reference_end|>
@article{lu2024sparse,
    title={Sparse Signal Reconstruction for Overdispersed Low-photon Count
  Biomedical Imaging Using $\ell_p$ Total Variation},
    author={Yu Lu and Roummel F. Marcia},
    journal={arXiv preprint arXiv:2408.16622},
    year={2024},
    doi={10.1109/ISBI56570.2024.10635788},
    archivePrefix={arXiv},
    eprint={2408.16622},
    primaryClass={eess.IV cs.CV eess.SP math.OC}
}