Inverse parameter and shape problem for an isotropic scatterer with two conductivity coefficients

TL;DR

This paper addresses the inverse problem of determining both the shape and conductivity coefficients of an isotropic scatterer using far-field data, introducing a stable direct sampling method validated through numerical examples.

Contribution

It establishes uniqueness for recovering two conductivity coefficients and the scatterer shape from fixed-frequency far-field data, and develops a stable direct sampling method for shape reconstruction.

Findings

Uniqueness of coefficient recovery from multi-frequency data

Development of a stable direct sampling method

Numerical validation of the method's effectiveness

Abstract

In this paper, we consider the direct and inverse problem for isotropic scatterers with two conductive boundary conditions. First, we show the uniqueness for recovering the coefficients from the known far-field data at a fixed incident direction for multiple frequencies. Then, we address the inverse shape problem for recovering the scatterer for the measured far-field data at a fixed frequency. Furthermore, we examine the direct sampling method for recovering the scatterer by studying the factorization for the far-field operator. The direct sampling method is stable with respect to noisy data and valid in two dimensions for partial aperture data. The theoretical results are verified with numerical examples to analyze the performance by the direct sampling method.