Remarks on the factorization and monotonicity method for inverse acoustic scatterings

TL;DR

This paper advances inverse acoustic scattering techniques by developing a new functional analysis theorem for the monotonicity method, enabling more flexible reconstruction schemes for targets with mixed boundary conditions.

Contribution

It introduces a general theorem that broadens the applicability of the monotonicity method, including for targets with mixed boundary conditions, extending previous approaches.

Findings

New theorem for the monotonicity method in inverse scattering

Reconstruction scheme for mixed boundary condition cracks

Enhanced ability to handle targets with different boundary conditions

Abstract

We study the factorization and monotonicity method for inverse acoustic scattering problems. Firstly, we give a new general functional analysis theorem for the monotonicity method. Comparing with the factorization method, the general theorem of the monotonicity generates reconstruction schemes under weaker {\it a priori} assumptions for unknown targets, and can directly deal with mixed problems so that the unknown targets have several different boundary conditions. Using the general theorem, we give the reconstruction scheme for the mixed crack that the Dirichlet boundary condition is imposed on one side of the crack and the Neumann boundary condition on the other side, which is a new extension of monotonicity method.