TITLE:
Statistical Inversion Based on Nonlinear Weighted Anisotropic Total Variational Model and Its Application in Electrical Impedance Tomography
AUTHORS:
Pengfei Qi
KEYWORDS:
Statistical Inverse Problem, Electrical Impedance Tomography, NWATV Prior, Markov Chain Monte Carlo Sampling
JOURNAL NAME:
Engineering,
Vol.16 No.1,
January
31,
2024
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.