新方法通过外部除法提升稀疏重建，改善泊松噪声下的图像恢复效果。
External Division of Two Bregman Proximity Operators for Poisson Inverse Problems
- 用双Bregman算子外部除法构造新算子，抑制L1正则偏差
- 在合成数据和图像修复任务中收敛更稳定，性能显著优于传统KL方法
- 适合处理含泊松噪声的稀疏信号恢复问题，如医学成像
本文提出一种从受泊松噪声污染的线性模型中恢复稀疏向量的新方法。首先，引入一种通过两个Bregman近端算子外部除法定义的新算子，可在促进稀疏解的同时缓解经典ℓ₁-范数正则化带来的估计偏差。该算子被嵌入已有的NoLips算法中，以即插即用方式替代标准Bregman近端算子。其次，通过两种互补的重表述揭示了所提外部除法算子的几何结构，分别在原始空间与对偶空间中提供清晰解释。数值实验表明，该方法相比传统的基于Kullback-Leibler（KL）的方案具有更稳定的收敛行为，并在合成数据和图像复原任务中取得显著更优的性能。
原文摘要 · Abstract (English)
This paper presents a novel method for recovering sparse vectors from linear models corrupted by Poisson noise. The contribution is twofold. First, an operator defined via the external division of two Bregman proximity operators is introduced to promote sparse solutions while mitigating the estimation bias induced by classical $\ell_1$-norm regularization. This operator is then embedded into the already established NoLips algorithm, replacing the standard Bregman proximity operator in a plug-and-play manner. Second, the geometric structure of the proposed external-division operator is elucidated through two complementary reformulations, which provide clear interpretations in terms of the primal and dual spaces of the Poisson inverse problem. Numerical tests show that the proposed method exhibits more stable convergence behavior than conventional Kullback-Leibler (KL)-based approaches and achieves significantly superior performance on synthetic data and an image restoration problem.
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