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arXiv · 2006.15634

Non-Stationary Multi-layered Gaussian Priors for Bayesian Inversion

Muhammad Emzir·Sari Lasanen·Zenith Purisha·Lassi Roininen·Simo Särkkä
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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.

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Muhammad Emzir, Sari Lasanen, Zenith Purisha, Lassi Roininen, Simo Särkkä. 2020-06-28. Non-Stationary Multi-layered Gaussian Priors for Bayesian Inversion. https://arxiv.org/abs/2006.15634

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