Non-Stationary Multi-layered Gaussian Priors for Bayesian Inversion
Abstract
In this article, we study Bayesian inverse problems with multi-layered Gaussian priors. We first describe the conditionally Gaussian layers in terms of a system of stochastic partial differential equations. We build the computational inference method using a finite-dimensional Galerkin method. We show that the proposed approximation has a convergence-in-probability property to the solution of the original multi-layered model. We then carry out Bayesian inference using the preconditioned Crank--Nicolson algorithm which is modified to work with multi-layered Gaussian fields. We show via numerical experiments in signal deconvolution and computerized X-ray tomography problems that the proposed method can offer both smoothing and edge preservation at the same time.
Cite
@article{arxiv.2006.15634,
title = {Non-Stationary Multi-layered Gaussian Priors for Bayesian Inversion},
author = {Muhammad Emzir and Sari Lasanen and Zenith Purisha and Lassi Roininen and Simo Särkkä},
journal= {arXiv preprint arXiv:2006.15634},
year = {2020}
}