Data completion algorithms and their applications in inverse acoustic scattering with limited-aperture backscattering data

TL;DR

This paper presents two fast, property-independent data completion algorithms for limited-aperture inverse acoustic scattering, enhancing object reconstruction through integration with existing imaging methods.

Contribution

The paper introduces novel, simple algorithms that relate limited to full-aperture data using the prolate matrix, applicable regardless of scatterer properties.

Findings

Algorithms are fast and simple to implement.

Effective in reconstructing objects from limited data.

Robust across various numerical examples.

Abstract

We introduce two data completion algorithms for the limited-aperture problems in inverse acoustic scattering. Both completion algorithms are independent of the topological and physical properties of the unknown scatterers. The main idea is to relate the limited-aperture data to the full-aperture data via the prolate matrix. The data completion algorithms are simple and fast since only the approximate inversion of the prolate matrix is involved. We then combine the data completion algorithms with imaging methods such as factorization method and direct sampling method for the object reconstructions. A variety of numerical examples are presented to illustrate the effectiveness and robustness of the proposed algorithms.