Shape and parameter identification by the linear sampling method for a restricted Fourier integral operator
Abstract
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.
Cite
@article{arxiv.2306.16199,
title = {Shape and parameter identification by the linear sampling method for a restricted Fourier integral operator},
author = {Lorenzo Audibert and Shixu Meng},
journal= {arXiv preprint arXiv:2306.16199},
year = {2024}
}