Bregman Plug-and-Play Priors

• URL: http://arxiv.org/abs/2202.02388v1
• Date: Fri, 4 Feb 2022 21:00:55 GMT
• Title: Bregman Plug-and-Play Priors
• Authors: Abdullah H. Al-Shabili, Xiaojian Xu, Ivan Selesnick, and Ulugbek S. Kamilov
• Abstract summary: We present a theoretical convergence result for. BPGM and demonstrate our algorithms on general linear inverse problems. We also present a theoretical convergence result for RED-BPGM and demonstrate our algorithms on linear inverse problems.
• Score: 12.834024732756465
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The past few years have seen a surge of activity around integration of deep learning networks and optimization algorithms for solving inverse problems. Recent work on plug-and-play priors (PnP), regularization by denoising (RED), and deep unfolding has shown the state-of-the-art performance of such integration in a variety of applications. However, the current paradigm for designing such algorithms is inherently Euclidean, due to the usage of the quadratic norm within the projection and proximal operators. We propose to broaden this perspective by considering a non-Euclidean setting based on the more general Bregman distance. Our new Bregman Proximal Gradient Method variant of PnP (PnP-BPGM) and Bregman Steepest Descent variant of RED (RED-BSD) replace the traditional updates in PnP and RED from the quadratic norms to more general Bregman distance. We present a theoretical convergence result for PnP-BPGM and demonstrate the effectiveness of our algorithms on Poisson linear inverse problems.

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