Statistical Inversion Based on Nonlinear Weighted Anisotropic Total Variational Model and Its Application in Electrical Impedance Tomography
- 1 School of Mathematics and Statistics, Shandong Normal University, Jinan, China
Abstract
Electrical impedance tomography (EIT) aims to reconstruct the conductivity distribution using the boundary measured voltage potential. Traditional regularization based method would suffer from error propagation due to the iteration process. The statistical inverse problem method uses statistical inference to estimate unknown parameters. In this article, we develop a nonlinear weighted anisotropic total variation (NWATV) prior density function based on the recently proposed NWATV regularization method. We calculate the corresponding posterior density function, i.e. , the solution of the EIT inverse problem in the statistical sense, via a modified Markov chain Monte Carlo (MCMC) sampling. We do numerical experiment to validate the proposed approach.
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