用可收敛的插件式算法解决泊松逆问题，适合高噪声医学成像。
A convergent Plug-and-Play Majorization-Minimization algorithm for Poisson inverse problems
- 基于极大似然与梯度去噪器结合，用预训练网络做正则化。
- 在中等噪声下表现达顶尖水平，高噪声时优势更明显。
- 理论保证收敛，适合核医学等高噪声场景应用。
本文提出一种用于泊松逆问题的新颖变分插件式算法。该方法最小化一个显式泛函，由Kullback-Leibler数据保真项与基于预训练神经网络的正则化项组成。通过结合经典似然最大化方法与基于梯度的去噪器最新进展，可在不牺牲收敛性保证的前提下使用预训练的高斯去噪器。算法采用极大化-极小化框架，确保收敛至驻点。数值实验表明，在中等噪声下的去卷积和断层扫描任务中达到当前最优性能，并在高噪声条件下展现出显著优势，特别适用于核医学应用。
原文摘要 · Abstract (English)
In this paper, we present a novel variational plug-and-play algorithm for Poisson inverse problems. Our approach minimizes an explicit functional which is the sum of a Kullback-Leibler data fidelity term and a regularization term based on a pre-trained neural network. By combining classical likelihood maximization methods with recent advances in gradient-based denoisers, we allow the use of pre-trained Gaussian denoisers without sacrificing convergence guarantees. The algorithm is formulated in the majorization-minimization framework, which guarantees convergence to a stationary point. Numerical experiments confirm state-of-the-art performance in deconvolution and tomography under moderate noise, and demonstrate clear superiority in high-noise conditions, making this method particularly valuable for nuclear medicine applications.
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