Year: 2024
Author: Weishi Yin, Zhaobin Xu, Pinchao Meng, Hongyu Liu
Annals of Applied Mathematics, Vol. 40 (2024), Iss. 2 : pp. 139–160
Abstract
In this paper, we are concerned with the inverse transmission eigenvalue problem to recover the shape as well as the constant refractive index of a penetrable medium scatterer. The linear sampling method is employed to determine the transmission eigenvalues within a certain wavenumber interval based on far-field measurements. Based on a prior information given by the linear sampling method, the neural network approach is proposed for the reconstruction of the unknown scatterer. We divide the wavenumber intervals into several subintervals, ensuring that each transmission eigenvalue is located in its corresponding subinterval. In each such subinterval, the wavenumber that yields the maximum value of the indicator functional will be included in the input set during the generation of the training data. This technique for data generation effectively ensures the consistent dimensions of model input. The refractive index and shape are taken as the output of the network. Due to the fact that transmission eigenvalues considered in our method are relatively small, certain super-resolution effects can also be generated. Numerical experiments are presented to verify the effectiveness and promising features of the proposed method in two and three dimensions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2024-0003
Annals of Applied Mathematics, Vol. 40 (2024), Iss. 2 : pp. 139–160
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Inverse transmission eigenvalue problem linear sampling method neural network super-resolution.