提出新型泊松反问题去噪器，提升图像恢复效果。
Learning Cocoercive Conservative Denoisers via Helmholtz Decomposition for Poisson Inverse Problems
- 基于赫尔姆霍兹分解设计可扩展的保守去噪器
- 在多个数据集上实现更优的视觉质量与定量指标
- 适合图像重建、医学成像等弱凸优化场景
基于深度去噪器的插件式（PnP）方法在图像恢复中表现优异，但通常要求保真项具有强凸性或光滑性，且去噪器为非扩张。这些假设在泊松反问题中不成立，且非扩张性会限制去噪性能。为此，本文提出一种共强制保守（CoCo）去噪器，允许残差扩张，从而提升去噪能力。通过广义赫尔姆霍兹分解，引入哈密顿正则化以保证保守性，以及谱正则化以确保共强制。我们证明，CoCo去噪器是弱凸函数的近端算子，支持隐式弱凸先验的重建模型。该模型的PnP方法全局收敛至驻点。大量实验表明，本方法在视觉质量和定量指标上均优于现有方法。
原文摘要 · Abstract (English)
Plug-and-play (PnP) methods with deep denoisers have shown impressive results in imaging problems. They typically require strong convexity or smoothness of the fidelity term and a (residual) non-expansive denoiser for convergence. These assumptions, however, are violated in Poisson inverse problems, and non-expansiveness can hinder denoising performance. To address these challenges, we propose a cocoercive conservative (CoCo) denoiser, which may be (residual) expansive, leading to improved denoising. By leveraging the generalized Helmholtz decomposition, we introduce a novel training strategy that combines Hamiltonian regularization to promote conservativeness and spectral regularization to ensure cocoerciveness. We prove that CoCo denoiser is a proximal operator of a weakly convex function, enabling a restoration model with an implicit weakly convex prior. The global convergence of PnP methods to a stationary point of this restoration model is established. Extensive experimental results demonstrate that our approach outperforms closely related methods in both visual quality and quantitative metrics.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。