FISTA迭代在去噪器驱动正则化下线性收敛
FISTA Iterates Converge Linearly for Denoiser-Driven Regularization
AI总结：
本文针对图像重建中的去噪驱动正则化，证明PnP-FISTA和RED-APG算法在线性逆问题与线性去噪器下，可通过简单谱分析建立迭代的全局线性收敛性。
摘要：
去噪驱动正则化在图像重建中的有效性已被广泛认可。该领域两个突出算法是即插即用（PnP）和去噪正则化（RED）。我们考虑PnP-FISTA和RED-APG两种特定算法，其正则化通过用强大去噪器替换FISTA算法中的近端算子来实现。已知FISTA的迭代收敛性极具挑战性，缺乏通用保证。然而，我们证明，对于线性逆问题和一类线性去噪器，通过简单谱分析即可建立PnP-FISTA和RED-APG迭代的全局线性收敛性。
英文摘要：
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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