Non-stationary multi-layered Gaussian priors for Bayesian inversion

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2020-12-03
Major/Subject
Mcode
Degree programme
Language
en
Pages
26
Series
Inverse Problems, Volume 37, issue 1
Abstract
In this article, we study Bayesian inverse problems with multi-layered Gaussian priors. The aim of the multi-layered hierarchical prior is to provide enough complexity structure to allow for both smoothing and edge-preserving properties at the same time. We first describe the conditionally Gaussian layers in terms of a system of stochastic partial differential equations. We then 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.
Description
Keywords
Bayesian inverse problem, Inverse problem, Multi-layer Gaussian field priors
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Citation
Emzir , M , Lasanen , S , Purisha , Z , Roininen , L & Särkkä , S 2020 , ' Non-stationary multi-layered Gaussian priors for Bayesian inversion ' , Inverse Problems , vol. 37 , no. 1 , 015002 . https://doi.org/10.1088/1361-6420/abc962