Short Communication: FISTA Iterates Converge Linearly for Denoiser-Driven Regularization
Arghya Sinha, Kunal N. Chaudhury · SIAM Journal on Imaging Sciences · 2025
Abstract. The effectiveness of denoising-driven regularization for image reconstruction has been widely recognized. Two prominent algorithms in this area are Plug-and-Play (PnP) and Regularization-by-Denoising (RED). We consider two specific algorithms, PnP-FISTA and RED-APG, where regularization is performed by replacing the proximal operator in the FISTA algorithm with a powerful denoiser. The iterate convergence of 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 PnP-FISTA and RED-APG can be established through simple spectral analysis.