Non-stationary multi-layered Gaussian priors for Bayesian inversion

Muhammad Emzir*, Sari Lasanen, Zenith Purisha, Lassi Roininen, Simo Särkkä

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)
82 Downloads (Pure)


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.

Original languageEnglish
Article number015002
Number of pages26
JournalInverse Problems
Issue number1
Publication statusPublished - 3 Dec 2020
MoE publication typeA1 Journal article-refereed


  • Bayesian inverse problem
  • Inverse problem
  • Multi-layer Gaussian field priors


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