Electrical Engineering and Systems Science > Image and Video Processing
[Submitted on 7 Apr 2020 (v1), last revised 14 Apr 2020 (this version, v2)]
Title:Plug-and-play ISTA converges with kernel denoisers
View PDFAbstract: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.
Submission history
From: Ruturaj Gavaskar [view email][v1] Tue, 7 Apr 2020 06:25:34 UTC (285 KB)
[v2] Tue, 14 Apr 2020 14:24:53 UTC (1,352 KB)
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