Comparison of statistical inversion with iteratively regularized Gauss Newton method for image reconstruction in electrical impedance tomography

Sanwar Ahmad, Thilo Strauss, Shyla Kupis, Taufiquar Khan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)

Abstract

In this paper, we investigate image reconstruction from the Electrical Impedance Tomography (EIT)problem using a statistical inversion method based on Bayes’ theorem and an Iteratively Regularized Gauss Newton (IRGN)method. We compare the traditional IRGN method with a new Pilot Adaptive Metropolis algorithm that (i)enforces smoothing constraints and (ii)incorporates a sparse prior. The statistical algorithm reduces the reconstruction error in terms of ℓ2 and ℓ1 norm in comparison to the IRGN method for the synthetic EIT reconstructions presented here. However, there is a trade-off between the reduced computational cost of the deterministic method and the higher resolution of the statistical algorithm. We bridge the gap between these two approaches by using the IRGN method to provide a more informed initial guess to the statistical algorithm. Our coupling procedure improves convergence speed and image resolvability of the proposed statistical algorithm.

Original languageEnglish
Pages (from-to)436-448
Number of pages13
JournalApplied Mathematics and Computation
Volume358
DOIs
Publication statusPublished - 1 Oct 2019
Externally publishedYes

Keywords

  • Bayesian inversion
  • Electrical impedance tomography
  • Markov Chain Monte Carlo method
  • Metropolis–Hastings algorithm
  • Statistical inversion

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