A Bayesian approach and total variation priors in 3D electrical impedance tomography
- Resource Type
- Conference
- Authors
- Kolehmainen, V.; Somersalo, E.; Vauhkonen, P.J.; Vauhkonen, M.; Kaipio, J.P.
- Source
- Proceedings of the 20th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. Vol.20 Biomedical Engineering Towards the Year 2000 and Beyond (Cat. No.98CH36286) Engineering in medicine and biology 1998 Engineering in Medicine and Biology Society, 1998. Proceedings of the 20th Annual International Conference of the IEEE. 2:1028-1031 vol.2 1998
- Subject
- Bioengineering
Bayesian methods
Tomography
Conductivity
Image reconstruction
Inverse problems
Density measurement
Random variables
Monte Carlo methods
Surface impedance
Surface reconstruction
- Language
- ISSN
- 1094-687X
The reconstruction of resistivity distribution in electrical impedance tomography (EIT) is a nonlinear ill-posed inverse problem which necessitates regularization. In this paper the regularized EIT problem is discussed from a Bayesian point of view. The basic idea in the Bayesian approach is to describe the resistivity distribution and voltage measurements as multivariate random variables. The regularization (prior information) is incorporated into the prior density. The solution for the inverse problem is obtained as a point estimate (typically mean or maximum) of the posterior density, which is the product of the prior density and the so-called likelihood density. A class of methods that can be used to compute the posterior mean are the so-called Markov chain Monte Carlo (MCMC) methods. These seem to be especially suitable when the prior information contain inequality constraints and nonsmooth functionals. In this paper the Bayesian approach to three dimensional EIT is examined with an example in which the retrieval of a "blocky" three dimensional resistivity distribution is carried out by using MCMC methods.