Abstract
In this paper, we consider the application and analysis of subspace migration technique for a fast imaging of a set of perfectly conducting cracks with small length in two-dimensional limited-aperture inverse scattering problem. In particular, an imaging function of subspace migration with asymmetric multistatic response matrix is designed, and its new mathematical structure is constructed in terms of an infinite series of Bessel functions and the range of incident and observation directions. This is based on the structure of left and right singular vectors linked to the nonzero singular values of MSR matrix and asymptotic expansion formula due to the existence of cracks. Investigated structure of imaging function indicates that imaging performance of subspace migration is highly related to the range of incident and observation directions. The simulation results with synthetic data polluted by random noise are exhibited to support investigated structure.
Highlights
This paper concerns the application of so-called subspace migration to determine the location of a set of small cracks from measured far-field data in limited-aperture problem
This framework was based on the asymptotic expansion formula in the presence of the crack and the structure of singular vectors of multistatic response (MSR) matrix under the assumption of coincident transmitter and receiver arrays
Throughout several real-world applications, such as biomedical imaging [6], synthetic aperture radar (SAR) [7], ground-penetrating radar (GPR) [8], photoacoustic tomography [9], the detection of inhomogeneities buried in the ground [10], physical optics [11], and crack detection of concrete void [12], the assumption of coincident transmitter and receiver arrays is not valid
Summary
This paper concerns the application of so-called subspace migration to determine the location of a set of small cracks from measured far-field data in limited-aperture problem. The main purposes of this contribution are designing an imaging function for imaging of a set of perfectly conducting cracks with small length in two-dimensional limited-aperture inverse scattering problem and exploring the mathematical structure of imaging function by constructing a relationship with an infinite series of Bessel functions of integer order and the range of incident and observation directions This is based on the structures of the left and right singular vectors of the asymmetric MSR matrix and the asymptotic expansion formula due to the presence of such cracks.
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