使用 $\ell_p$ 全变分进行过分散低光子计数生物医学成像的稀疏信号重建
Sparse Signal Reconstruction for Overdispersed Low-photon Count Biomedical Imaging Using $\ell_p$ Total Variation
AI总结：
本文在负二项统计模型框架内研究了 $\ell_p$ 拟半范数及各向同性和各向异性 $\ell_p$ TV 拟半范数，通过基于梯度的优化方法求解，有效提升了低光子计数生物医学成像的稀疏信号重建效果。
摘要：
负二项模型推广了泊松分布模型，可应用于涉及低光子信号恢复的领域，包括医学成像。近期研究探讨了负二项模型的几种正则化项，如 $0 < p < 1$ 的 $\ell_p$ 拟范数、$\ell_1$ 范数，以及用于促进信号恢复稀疏性的全变分（TV）拟半范数。这些惩罚项已被证明能改善图像重建效果。本文在负二项统计模型框架内，研究了 $\ell_p$ 拟半范数，以及各向同性和各向异性 $\ell_p$ TV 拟半范数。该问题可表述为优化问题，我们使用基于梯度的方法求解。我们比较了负二项和泊松统计模型在使用 $\ell_p$ TV 拟半范数及常见惩罚项下的表现。实验结果突显了所提方法的有效性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
