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

arXiv:2510.27211 · math.OC, eess.SP, stat.ML · Submitted 2025-10-31 · Read on arXiv

math.OC, eess.SP, stat.ML

Submitted: 2025-10-31

Updated: 2026-06-15

Journal ref: IEEE Transactions on Computational Imaging, vol. 12, pp. 1205-1214, Jun. 2026

DOI: 10.1109/TCI.2026.3707068

Code: https://github.com/sparsity-group/pnpmmse

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Inverse Problem — 15× in this paper · explained in 2 episodes
• Fidelity — 13× in this paper · explained in 2 episodes
• Regularization — 8× in this paper · explained in 3 episodes
• Convergence Guarantees — 4× in this paper · explained in 3 episodes
• Adam — 3× in this paper · explained in 2 episodes
• Objective Function — 3× in this paper · explained in 2 episodes
• Sparsity — 3× in this paper · explained in 4 episodes
• Activation Function — 1× in this paper · explained in 1 episode
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Models — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Interpretability — 1× in this paper · explained in 15 episodes
• Parsimony — 1× in this paper · explained in 2 episodes
• Score Function — 1× in this paper · explained in 4 episodes
• Selection Bias — 1× in this paper · explained in 4 episodes

Sources

• Image Restoration Using Convolutional Auto-encoders with Symmetric Skip Connections
• Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisation

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