TY - JOUR
T1 - On a Hybrid Method for Inverse Transmission Eigenvalue Problems
AU - Yin , Weishi
AU - Xu , Zhaobin
AU - Meng , Pinchao
AU - Liu , Hongyu
JO - Annals of Applied Mathematics
VL - 2
SP - 139
EP - 160
PY - 2024
DA - 2024/05
SN - 40
DO - http://doi.org/10.4208/aam.OA-2024-0003
UR - https://global-sci.org/intro/article_detail/aam/23098.html
KW - Inverse transmission eigenvalue problem, linear sampling method, neural network, super-resolution.
AB - <p style="text-align: justify;">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.</p>