Single Mode Multi-frequency Factorization Method for the Inverse Source Problem in Acoustic Waveguides

TL;DR

This paper develops a novel multi-frequency factorization method for the inverse source problem in acoustic waveguides, providing theoretical justification and efficient algorithms for imaging sources using a single propagating mode.

Contribution

It introduces a multi-frequency far-field operator that accounts for waveguide dispersion, and establishes a rigorous factorization-based characterization of source support.

Findings

The method accurately images the source support in waveguides.

Numerical examples demonstrate the effectiveness of the proposed sampling methods.

The approach handles non-linear dispersion relations in waveguides.

Abstract

This paper investigates the inverse source problem with a single propagating mode at multiple frequencies in an acoustic waveguide. The goal is to provide both theoretical justifications and efficient algorithms for imaging extended sources using the sampling methods. In contrast to the existing far/near field operator based on the integral over the space variable in the sampling methods, a multi-frequency far-field operator is introduced based on the integral over the frequency variable. This far-field operator is defined in a way to incorporate the possibly non-linear dispersion relation, a unique feature in waveguides. The factorization method is deployed to establish a rigorous characterization of the range support which is the support of source in the direction of wave propagation. A related factorization-based sampling method is also discussed. These sampling methods are shown to be capable of imaging the range support of the source. Numerical examples are provided to illustrate the performance of the sampling methods, including an example to image a complete sound-soft block.