Friday, 16 May 2014

EIT & GMRF paper published in Inverse Problems and Imaging

Our paper on electrical impedance tomography and Gaussian Markov random field priors has been published in May issue of Inverse Problems of Imaging. You can find the paper at the IPI website http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=9912. This paper was discussed in an earlier post at http://kaira.sgo.fi/2014/03/latest-results-bayesian-inversion-on.html. Below we have the reference and abstract of the paper as well as one image, where we have visualised samples of the anisotropic and inhomogeneous Gaussian Markov random fields.

The final reference is:

L. Roininen, J. M. J. Huttunen and S. Lasanen, Whittle-Matérn priors for Bayesian statistical inversion with applications in electrical impedance tomography, Inverse Problems and Imaging, (2014) 561-586.

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 Whittle-Matérn random field in 2. 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-Matérn 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.


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