Papers › FISTA Iterates Converge Linearly for Denoiser-Driven Regularization
FISTA Iterates Converge Linearly for Denoiser-Driven Regularization
Arghya Sinha, Kunal N. Chaudhury
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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.
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