Plug-and-Play ISTA Converges with Kernel Denoisers

Gavaskar, RG and Chaudhury, KN (2020) Plug-and-Play ISTA Converges with Kernel Denoisers. In: IEEE Signal Processing Letters, 27 . pp. 610-614.

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Abstract

Plug-and-play (PnP) method is a recent paradigm for image regularization, where the proximal operator (associated with some given regularizer) in an iterative algorithm is replaced with a powerful denoiser. Algorithmically, this involves repeated inversion (of the forward model) and denoising until convergence. Remarkably, PnP regularization produces promising results for several restoration applications. However, a fundamental question in this regard is the theoretical convergence of the PnP iterations, since the algorithm is not strictly derived from an optimization framework. This question has been investigated in recent works, but there are still many unresolved problems. For example, it is not known if convergence can be guaranteed if we use generic kernel denoisers (e.g. nonlocal means) within the ISTA framework (PnP-ISTA). We prove that, under reasonable assumptions, fixed-point convergence of PnP-ISTA is indeed guaranteed for linear inverse problems such as deblurring, inpainting and superresolution (the assumptions are verifiable for inpainting). We compare our theoretical findings with existing results, validate them numerically, and explain their practical relevance.

Item Type:	Journal Article
Publication:	IEEE Signal Processing Letters
Publisher:	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Additional Information:	The copyright of this article belongs to IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Keywords:	Iterative methods, Forward modeling; Image regularization; Iterative algorithm; Linear inverse problems; Non-local means; Optimization framework; Plug and play; Super resolution, Inverse problems
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	23 Jun 2020 09:02
Last Modified:	23 Jun 2020 09:02
URI:	http://eprints.iisc.ac.in/id/eprint/65505

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