Regularization of the Factorization Method with Applications to Inverse Scattering

TL;DR

This paper introduces a regularized factorization method for inverse shape problems in acoustic scattering, improving stability and simplicity in reconstructing unknown structures with minimal prior information.

Contribution

It presents a novel regularization approach for the factorization method, enhancing stability and applicability in inverse scattering problems.

Findings

Regularized method improves numerical stability.

Successfully applied to acoustic inverse scattering.

Numerical examples demonstrate effectiveness with synthetic data.

Abstract

Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In general, qualitative methods seek to reconstruct the shape of an unknown object using little to no a priori information. The regularized factorization method presented here seeks to avoid numerical instabilities in the inversion algorithm. This allows one to recover unknown structures in a computationally simple and analytically rigorous way. We will discuss the theory and application of the regularized factorization method to examples coming from acoustic inverse scattering. Numerical examples will also be presented using synthetic data to show the applicability of the method.