# FISTA Iterates Converge Linearly for Denoiser-Driven Regularization

arXiv: https://arxiv.org/abs/2411.10808 · HTML: https://mlsanity.com/paper/2411.10808/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2024.

## Built on by (most cited first, 1 of 1)

- [Solving Imaging Inverse Problems Using Plug-and-Play Denoisers: Regularization and Optimization Perspectives](https://mlsanity.com/paper/2509.03475/) (2025)

## Abstract (arXiv)

The effectiveness of denoising-driven regularization for image reconstruction has been widely recognized. Two prominent algorithms in this area are Plug-and-Play (textttPnP) and Regularization-by-Denoising (textttRED). We consider two specific algorithms textttPnP-FISTA and textttRED-APG, where regularization is performed by replacing the proximal operator in the textttFISTA algorithm with a powerful denoiser. The iterate convergence of textttFISTA 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 textttPnP-FISTA and textttRED-APG can be established through simple spectral analysis.