The Linearized Inverse Problem in Multifrequency Electrical Impedance Tomography

TL;DR

This paper analyzes the linearized inverse problem in multifrequency electrical impedance tomography, proposing methods for accurate reconstruction of tissue inclusions despite modeling errors and partial spectral knowledge.

Contribution

It introduces a comprehensive analysis of the linearized inverse problem, including reconstruction techniques for known and partially known spectral profiles, and develops a robust group sparse recovery algorithm.

Findings

Multifrequency approach reduces modeling errors.

Difference imaging effectively handles partial spectral knowledge.

Numerical simulations validate the proposed methods.

Abstract

This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency dependence, as is often seen in biological tissues. We discuss reconstruction methods for both fully known and partially known spectral profiles, and demonstrate in the latter case the successful employment of difference imaging. We also study the reconstruction with an imperfectly known boundary, and show that the multifrequency approach can eliminate modeling errors and recover almost all inclusions. In addition, we develop an efficient group sparse recovery algorithm for the robust solution of related linear inverse problems. Several numerical simulations are presented to illustrate and validate the approach.