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Somersalo, E., Kaipio, J.P., Vauhkonen, M., Baroudi, D. and Jarvenpaa, S. (1997) Impedance Imaging and Markov Chain Monte Carlo Methods. Proc SPIE’s 42nd Annual Meeting, Computational, Experimental and Numerical Methods for Solving Illposed Inverse Imaging Problems: Medical and Nonmedical Applications, San Diego, USA, June 27-August 1, 1997, 175-185.

has been cited by the following article:

• 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.