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Comparison of statistical inversion with iteratively regularized Gauss Newton method for image reconstruction in electrical impedance tomography. (English) Zbl 1428.78036

Summary: 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 \(\ell_2\) and \(\ell_1\) 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.

MSC:

78M99 Basic methods for problems in optics and electromagnetic theory
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
65C05 Monte Carlo methods
78A55 Technical applications of optics and electromagnetic theory
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
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