Deep Neural Network-Oriented Indicator Method for Inverse Scattering Problems Using Partial Data

Authors

Yule Lin, Jinan University
Xiaoyi Yan, Jinan University
Jiguang Sun, Michigan Technological UniversityFollow
Juan Liu, Jinan University

Document Type

Article

Publication Date

2-7-2024

Department

Department of Mathematical Sciences

Abstract

We consider the inverse scattering problem to reconstruct an obstacle using partial far-field data due to one incident wave. A simple indicator function, which is negative inside the obstacle and positive outside of it, is constructed and then learned using a deep neural network (DNN). The method is easy to implement and effective as demonstrated by numerical examples. Rather than developing sophisticated network structures for the classical inverse operators, we reformulate the inverse problem as a suitable operator such that standard DNNs can learn it well. The idea of the DNN-oriented indicator method can be generalized to treat other partial data inverse problems.

Publisher's Statement

Copyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. Publisher’s version of record: https://doi.org/10.3390/math12040522

Publication Title

Mathematics

Recommended Citation

Lin, Y., Yan, X., Sun, J., & Liu, J. (2024). Deep Neural Network-Oriented Indicator Method for Inverse Scattering Problems Using Partial Data. Mathematics, 12(4). http://doi.org/10.3390/math12040522
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/597

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Version

Publisher's PDF