证明了核去噪器在图像重建中线性收敛，突破对称性限制。
Linear Convergence of Plug-and-Play Algorithms with Kernel Denoisers
- 统一框架分析对称与非对称核去噪器的收敛性。
- 给出插值、去模糊、超分辨率任务的收敛速率定量边界。
- 为非对称场景提供理论支持，适合算法设计者参考。
基于去噪器的图像重建展现出巨大潜力，尤其在插件式（Plug-and-Play, PnP）框架中。PnP 将强去噪器作为隐式正则项嵌入到如ISTA和ADMM等近端算法中。本文聚焦于线性逆问题下使用核去噪器的PnP迭代收敛性。先前工作表明，在去噪器与线性前向算子满足特定条件时，标准PnP的更新算子对称核去噪器是压缩的，从而可利用压缩映射定理建立全局线性收敛。本文进一步构建统一框架，证明对称与非对称核去噪器均可实现全局线性收敛。此外，推导出插值、去模糊及超分辨率任务中收缩因子（收敛速率）的量化界，并通过数值实验验证理论结果。
原文摘要 · Abstract (English)
The use of denoisers for image reconstruction has shown significant potential, especially for the Plug-and-Play (PnP) framework. In PnP, a powerful denoiser is used as an implicit regularizer in proximal algorithms such as ISTA and ADMM. The focus of this work is on the convergence of PnP iterates for linear inverse problems using kernel denoisers. It was shown in prior work that the update operator in standard PnP is contractive for symmetric kernel denoisers under appropriate conditions on the denoiser and the linear forward operator. Consequently, we could establish global linear convergence of the iterates using the contraction mapping theorem. In this work, we develop a unified framework to establish global linear convergence for symmetric and nonsymmetric kernel denoisers. Additionally, we derive quantitative bounds on the contraction factor (convergence rate) for inpainting, deblurring, and superresolution. We present numerical results to validate our theoretical findings.
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