A direct sampling method for magnetic induction tomography

TL;DR

This paper introduces a fast and efficient direct sampling method for magnetic induction tomography, utilizing point spread functions with explicit formulas and proven decay properties to improve imaging speed and accuracy.

Contribution

The paper presents a novel direct sampling algorithm for MIT that is simple, fast, and theoretically grounded, with explicit point spread functions and decay analysis.

Findings

The method achieves accurate imaging results.

Numerical experiments confirm efficiency and precision.

Point spread functions decay with distance, supporting the algorithm's validity.

Abstract

This paper proposes a direct sampling method for the inverse problem of magnetic induction tomography (MIT). Our approach defines a class of point spread functions with explicit expressions, which are computed via inner products, leading to a simple and fast imaging process. We then prove that these point spread functions decay with distance, establishing the theoretical basis of the algorithm. Specific expressions for special cases are also derived to visually demonstrate their attenuation pattern. Numerical experimental results further confirm the efficiency and accuracy of the proposed algorithm.