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A novel study on subspace migration for imaging of a sound-hard arc. (English) Zbl 1397.65240

Summary: 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.

MSC:

65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
76Q05 Hydro- and aero-acoustics
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35R30 Inverse problems for PDEs
33C05 Classical hypergeometric functions, \({}_2F_1\)
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References:

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