Co-inversion of a scattering cavity and its internal sources: uniqueness, decoupling and imaging

TL;DR

This paper introduces a novel, efficient method for simultaneously reconstructing a sound-soft cavity and its internal sources from total-field data, using decoupling into two linear inverse problems with proven uniqueness and stability.

Contribution

The paper presents a new decoupling technique for co-inversion of cavities and sources, enabling fast and stable reconstruction via linear integral equations and established methods.

Findings

Decoupling reduces the co-inversion to two simpler inverse problems.

The method is proven to be unique and stable.

Numerical examples demonstrate effectiveness and feasibility.

Abstract

This paper concerns the simultaneous reconstruction of a sound-soft cavity and its excitation sources from the total-field data. Using the single-layer potential representations on two measurement curves, this co-inversion problem can be decoupled into two inverse problems: an inverse cavity scattering problem and an inverse source problem. This novel decoupling technique is fast and easy to implement since it is based on a linear system of integral equations. Then the uncoupled subproblems are respectively solved by the modified optimization and sampling method. We also establish the uniqueness of this co-inversion problem and analyze the stability of our method. Several numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed method.