  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.

Numerical Analysis