Projects per year
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.
- Bayesian inverse problem
- Inverse problem
- Multi-layer Gaussian field priors
04/09/2019 → 31/12/2022
Project: Academy of Finland: Other research funding