Shape and parameter identification by the linear sampling method for a restricted Fourier integral operator

In this paper we provide a new linear sampling method based on the same data but a different definition of the data operator for two inverse problems: the multi-frequency inverse source problem for a fixed observation direction and the Born inverse scattering problems. We show that the associated re...

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Bibliographic Details
Published in:Inverse problems 2024-09, Vol.40 (9), p.95007
Main Authors: Audibert, Lorenzo, Meng, Shixu
Format: Article
Language:English
Subjects:
inverse source and scattering problems
linear sampling method
parameter identification
prolate spheroidal wave functions
shape identification
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Summary:In this paper we provide a new linear sampling method based on the same data but a different definition of the data operator for two inverse problems: the multi-frequency inverse source problem for a fixed observation direction and the Born inverse scattering problems. We show that the associated regularized linear sampling indicator converges to the average of the unknown in a small neighborhood as the regularization parameter approaches to zero. We develop both a shape identification theory and a parameter identification theory which are stimulated, analyzed, and implemented with the help of the prolate spheroidal wave functions and their generalizations. We further propose a prolate-based implementation of the linear sampling method and provide numerical experiments to demonstrate how this linear sampling method is capable of reconstructing both the shape and the parameter.
ISSN:0266-5611
1361-6420
DOI:10.1088/1361-6420/ad5e18