Subgradient Langevin Methods for Sampling from Non-smooth Potentials

作     者：Habring, Andreas Holler, Martin Pock, Thomas 

作者机构：Department of Mathematics and Scientific Computing University of Graz Austria Institute of Computer Graphics and Vision Graz University of Technology Austria 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2023年

核心收录：

主　　题：Inverse problems 

摘      要：This paper is concerned with sampling from probability distributions π on Rd admitting a density of the form π(x) ∝ e−U(x), where U(x) = F(x) + G(Kx) with K being a linear operator and G being non-differentiable. Two different methods are proposed, both employing a subgradient step with respect to G ◦ K, but, depending on the regularity of F, either an explicit or an implicit gradient step with respect to F. For both methods, non-asymptotic convergence proofs are provided, with improved convergence results for more regular F. Further, numerical experiments are conducted for simple 2D examples, illustrating the convergence rates, and for examples of Bayesian imaging, showing the practical feasibility of the proposed methods for high dimensional *** Codes 65C40, 65C05, 68U10, 65C60 Copyright © 2023, The Authors. All rights reserved.