A1 Journal article (refereed), original research

Whittle-Matérn priors for Bayesian statistical inversion with applications in electrical impedance tomography


Publication Details
Authors: Roininen Lassi, Huttunen Janne M. J., Lasanen Sari
Publisher: American Institute of Mathematical Sciences (AIMS)
Publication year: 2014
Language: English
Related journal or series: Inverse Problems and Imaging
Volume number: 8
Issue number: 2
Start page: 506
End page: 586
Number of pages: 81
ISSN: 1930-8337
eISSN: 1930-8345
JUFO level of this publication: 2
Open Access: Not an Open Access publication

Abstract

We study flexible and proper smoothness priors for Bayesian statistical inverse problems by using Whittle-Matérn Gaussian random fields. We review earlier results on finite-difference approximations of certain WhittleMat´ern random field in R2 . Then we derive finite-element method approximations and show that the discrete approximations can be expressed as solutions of sparse stochastic matrix equations. Such equations are known to be computationally efficient and useful in inverse problems with a large number of unknowns. The presented construction of Whittle-Mat´ern correlation functions allows both isotropic or anisotropic priors with adjustable parameters in correlation length and variance. These parameters can be used, for example, to model spatially varying structural information of unknowns. As numerical examples, we apply the developed priors to two-dimensional electrical impedance tomography problems with one- and two-dimensional unknowns.


Last updated on 2019-07-01 at 20:26