A non-iterative method for the electrical impedance tomography based on joint sparse recovery

TL;DR

This paper introduces a non-iterative joint sparse recovery method for electrical impedance tomography to efficiently detect multiple small anomalies from boundary measurements, improving over traditional iterative techniques.

Contribution

It presents a novel non-iterative algorithm based on joint sparse recovery for inverse conductivity problems, capable of reconstructing small and extended anomalies.

Findings

Outperforms linearized methods in accuracy

More efficient than iterative algorithms

Successfully reconstructs multiple anomalies in simulations

Abstract

The purpose of this paper is to propose a non-iterative method for the inverse conductivity problem of recovering multiple small anomalies from the boundary measurements. When small anomalies are buried in a conducting object, the electric potential values inside the object can be expressed by integrals of densities with a common sparse support on the location of anomalies. Based on this integral expression, we formulate the reconstruction problem of small anomalies as a joint sparse recovery and present an efficient non-iterative recovery algorithm of small anomalies. Furthermore, we also provide a slightly modified algorithm to reconstruct an extended anomaly. We validate the effectiveness of the proposed algorithm over the linearized method and the MUSIC algorithm by numerical simulations.