证明了去噪器驱动的图像重建算法能线性收敛，为实际应用提供理论保障。
FISTA Iterates Converge Linearly for Denoiser-Driven Regularization
- 用谱分析方法，将去噪器替换梯度下降中的近端算子
- 在线性逆问题下，两类算法迭代过程全局线性收敛
- 适合关注图像重建理论保证的研究者和工程师
去噪器驱动的正则化在图像重建中效果显著，代表性算法包括Plug-and-Play（PnP）和Regularization-by-Denoising（RED）。本文研究PnP-FISTA与RED-APG两种算法，将FISTA中的近端算子替换为强去噪器。尽管FISTA迭代收敛性难以保证，但本文在处理线性逆问题且使用一类线性去噪器时，通过简单的谱分析，建立了PnP-FISTA与RED-APG迭代序列的全局线性收敛性。
原文摘要 · Abstract (English)
The effectiveness of denoising-driven regularization for image reconstruction has been widely recognized. Two prominent algorithms in this area are Plug-and-Play ($\texttt{PnP}$) and Regularization-by-Denoising ($\texttt{RED}$). We consider two specific algorithms $\texttt{PnP-FISTA}$ and $\texttt{RED-APG}$, where regularization is performed by replacing the proximal operator in the $\texttt{FISTA}$ algorithm with a powerful denoiser. The iterate convergence of $\texttt{FISTA}$ is known to be challenging with no universal guarantees. Yet, we show that for linear inverse problems and a class of linear denoisers, global linear convergence of the iterates of $\texttt{PnP-FISTA}$ and $\texttt{RED-APG}$ can be established through simple spectral analysis.
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