High-order regularized regression in Electrical Impedance Tomography

TL;DR

This paper introduces a high-order regularized regression method for electrical impedance tomography, improving inverse problem solutions by accounting for nonlinearities with second-order accuracy.

Contribution

It presents a novel nonlinear forward model formulation and a high-order approximation approach for the inverse problem, enhancing accuracy over linear methods.

Findings

Superior results compared to linear regression methods

Effective handling of nonlinear inverse problems

Moderate computational complexity increase

Abstract

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral transform, that maps changes in the electrical properties of a domain to their respective variations in boundary data. Using perturbation theory the transform is approximated to yield a high-order misfit unction which is then used to derive a regularized inverse problem. In particular, we consider the nonlinear problem to second-order accuracy, hence our approximation method improves upon the local linearization of the forward mapping. The inverse problem is approached using Newton's iterative algorithm and results from simulated experiments are presented. With a moderate increase in computational complexity, the method yields superior results compared to those of regularized linear regression and can be implemented to address the nonlinear inverse problem.