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Shape reconstruction methods with incomplete data

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Abstract

Linearized inverse scattering methods are applied to the shape reconstruction of defects in elastic solids. The linearized methods are based on the Born approximation in the low frequency range and the Kirchhoff approximation in the high frequency range. The experimental measurement is performed to collect the scattering data from defects. The processed data from the measurement are fed into the linearized methods and the shape of the defect is reconstructed by two linearized methods. The importance of scattering data in the low frequency range is pointed out not only for Born inversion but also for Kirchhoff inversion. In the ultrasonic measurement for the real structure, the access points of the sensor may be limited to one side of the structural surfaces and a part of the surface. From the viewpoint of application, the incomplete scattering data are used as inputs for the shape reconstruction methods and the effect of the sensing points are discussed.

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