Direct sampling method via Landweber iteration for an absorbing scatterer with a conductive boundary

TL;DR

This paper introduces a novel direct sampling method combining Landweber iteration and the factorization method for reconstructing absorbing scatterers with conductive boundaries, validated through theoretical analysis and numerical experiments.

Contribution

It establishes a new Landweber-based direct sampling indicator and connects it with the factorization method for improved inverse shape reconstruction.

Findings

The new method provides stable reconstructions.

Theoretical connection between Landweber iteration and factorization method.

Numerical examples demonstrate effective reconstruction performance.

Abstract

In this paper, we consider the inverse shape problem of recovering isotropic scatterers with a conductive boundary condition. Here, we assume that the measured far-field data is known at a fixed wave number. Motivated by recent work, we study a new direct sampling indicator based on the Landweber iteration and the factorization method. Therefore, we prove the connection between these reconstruction methods. The method studied here falls under the category of qualitative reconstruction methods where an imaging function is used to recover the absorbing scatterer. We prove stability of our new imaging function as well as derive a discrepancy principle for recovering the regularization parameter. The theoretical results are verified with numerical examples to show how the reconstruction performs by the new Landweber direct sampling method.