A novel study on subspace migration for imaging of a sound-hard arc

TL;DR

This paper investigates how the choice of test vectors affects subspace migration imaging of sound-hard arcs, introducing a new mathematical structure based on Bessel functions that links imaging performance to the arc shape.

Contribution

It presents a novel mathematical structure of the imaging function for subspace migration, highlighting the impact of test vector selection on imaging quality.

Findings

The new structure is supported by simulation results with noisy data.

Imaging performance is highly related to the unknown shape of the arc.

The structure involves Bessel functions of orders 0, 1, and 2.

Abstract

In this study, the influence of a test vector selection used in subspace migration to reconstruct the shape of a sound-hard arc in a two-dimensional inverse acoustic problem is considered. In particular, a new mathematical structure of imaging function is constructed in terms of the Bessel functions of the order 0, 1, and 2 of the first kind based on the structure of singular vectors linked to the nonzero singular values of a Multi-Static Response (MSR) matrix. This structure indicates that imaging performance of subspace migration is highly related to the unknown shape of arc. The simulation results with noisy data indicate support for the derived structure.