Nonasymptotic Convergence Rates for Plug-and-Play Methods With MMSE Denoisers

arXiv — stat.MLWednesday, November 5, 2025 at 5:00:00 AM
A recent article published on arXiv in the stat.ML category examines the nonasymptotic convergence rates of plug-and-play methods that utilize minimum-mean-squared-error (MMSE) denoisers under Gaussian noise conditions. The study emphasizes that the MMSE denoiser can be represented as a proximal operator, a key insight for analyzing the convergence behavior of these methods. This representation not only aids in understanding convergence rates but also uncovers the structure of the associated regularizer linked to the denoiser. By revealing this structure, the research provides a deeper theoretical foundation for plug-and-play algorithms in the presence of Gaussian noise. These findings contribute to the broader field of machine learning by clarifying how MMSE denoisers function within iterative schemes. The article thus offers valuable context for future developments in denoising techniques and their convergence properties.
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