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On the Contractivity of Plug-and-Play Operators

Athalye, CD and Chaudhury, KN and Kumar, B (2023) On the Contractivity of Plug-and-Play Operators. In: IEEE Signal Processing Letters, 30 . pp. 1447-1451.

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Official URL: https://doi.org/10.1109/LSP.2023.3323248


In plug-and-play (PnP) regularization, the proximal operator in algorithms such as ISTA and ADMM is replaced by a powerful denoiser. This formal substitution works surprisingly well in practice. In fact, PnP has been shown to give state-of-the-art results for various imaging applications. The empirical success of PnP has motivated researchers to understand its theoretical underpinnings and, in particular, its convergence. It was shown in prior work that for kernel denoisers such as the nonlocal means, PnP-ISTA provably converges under some strong assumptions on the forward model. The present work is motivated by the following questions: Can we relax the assumptions on the forward model? Can the convergence analysis be extended to PnP-ADMM? Can we estimate the convergence rate? In this letter, we resolve these questions using the contraction mapping theorem: i) for symmetric denoisers, we show that (under mild conditions) PnP-ISTA and PnP-ADMM exhibit linear convergence; and ii) for kernel denoisers, we show that PnP-ISTA and PnP-ADMM converge linearly for image inpainting. We validate our theoretical findings using reconstruction experiments. © 1994-2012 IEEE.

Item Type: Journal Article
Publication: IEEE Signal Processing Letters
Publisher: Institute of Electrical and Electronics Engineers Inc.
Additional Information: The copyright for this article belongs to Author.
Keywords: Image denoising; Image reconstruction; Mapping, ADMM; Contraction mappings; Convergence; Eigenvalue and eigenfunctions; Images reconstruction; ISTA; Kernel; Kernel denoiser; Plug-and-play; Signal processing algorithms; Superresolution; Symmetric denoiser; Symmetric matrices; Symmetrics, Eigenvalues and eigenfunctions
Department/Centre: Division of Electrical Sciences > Electrical Engineering
Date Deposited: 04 Mar 2024 09:59
Last Modified: 04 Mar 2024 09:59
URI: https://eprints.iisc.ac.in/id/eprint/84403

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