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Xiaojian Xu, Yu Sun, Jiaming Liu, Brendt Wohlberg and Ulugbek S. Kamilov, "Provable Convergence of Plug-and-Play Priors with MMSE denoisers", IEEE Signal Processing Letters, doi:10.1109/LSP.2020.3006390, 2020

Abstract

Plug-and-play priors (PnP) is a methodology for regularized image reconstruction that specifies the prior through an image denoiser. While PnP algorithms are well understood for denoisers performing maximum a posteriori probability (MAP) estimation, they have not been analyzed for the minimum mean squared error (MMSE) denoisers. This letter addresses this gap by establishing the first theoretical convergence result for the iterative shrinkage/thresholding algorithm (ISTA) variant of PnP for MMSE denoisers. We show that the iterates produced by PnP-ISTA with an MMSE denoiser converge to a stationary point of some global cost function. We validate our analysis on sparse signal recovery in compressive sensing by comparing two types of denoisers, namely the exact MMSE denoiser and the approximate MMSE denoiser obtained by training a deep neural net.

BibTeX Entry

@article{xu-2020-provable,
author = {Xiaojian Xu and Yu Sun and Jiaming Liu and Brendt Wohlberg and Ulugbek S. Kamilov},
title = {Provable Convergence of Plug-and-Play Priors with MMSE denoisers},
year = {2020},
urlpdf = {http://arxiv.org/pdf/2005.07685},
urlhtml = {http://arxiv.org/abs/2005.07685},
journal = {IEEE Signal Processing Letters},
doi = {10.1109/LSP.2020.3006390}
}