Non-Stationary Multi-layered Gaussian Priors for Bayesian Inversion

06/28/2020 ∙ by Muhammad Emzir, et al. ∙ 0

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.



There are no comments yet.


page 24

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.