An efficient hierarchical Bayesian method for the Kuopio tomography challenge 2023

TL;DR

This paper introduces a hybrid hierarchical Bayesian method based on the PS-IAS algorithm for nonlinear EIT reconstruction, demonstrating efficiency and detailed implementation for the Kuopio tomography challenge 2023.

Contribution

A novel hybrid Bayesian algorithm tailored for nonlinear EIT inverse problems, with detailed parameter selection and performance analysis on challenge data.

Findings

Efficient reconstruction times across different parameter settings.

Successful application to the Kuopio tomography challenge dataset.

Detailed implementation guidelines for the hybrid PS-IAS method.

Abstract

The aim of Electrical Impedance Tomography (EIT) is to determine the electrical conductivity distribution inside a domain by applying currents and measuring voltages on its boundary. Mathematically, the EIT reconstruction task can be formulated as a non-linear inverse problem. The Bayesian inverse problems framework has been applied expensively to solutions of the EIT inverse problem, in particular in the cases when the unknown conductivity is believed to be blocky. Recently, the Sparsity Promoting Iterative Alternating Sequential (PS-IAS) algorithm, originally proposed for the solution of linear inverse problems, has been adapted for the non linear case of EIT reconstruction in a computationally efficient manner. Here we introduce a hybrid version of the SP-IAS algorithms for the nonlinear EIT inverse problem, providing a detailed description of the implementation details, with a specific focus on parameters selection. The method is applied to the 2023 Kuopio Tomography Challenge dataset, with a comprehensive report of the running times for the different cases and parameter selections.