Sampling type method combined with deep learning for inverse scattering with one incident wave

TL;DR

This paper introduces a fast, noise-robust sampling method combined with deep learning to improve the accuracy of inverse scattering reconstructions from a single incident wave, applicable to near and far field data.

Contribution

It develops a novel imaging functional for sampling that is integrated with a deep neural network, enhancing reconstruction quality and efficiency in inverse scattering problems.

Findings

The combined method improves reconstruction accuracy significantly.

It can invert limited aperture experimental data without transfer training.

The imaging functional's decay rate and robustness are analytically characterized.

Abstract

We consider the inverse problem of determining the geometry of penetrable objects from scattering data generated by one incident wave at a fixed frequency. We first study an orthogonality sampling type method which is fast, simple to implement, and robust against noise in the data. This sampling method has a new imaging functional that is applicable to data measured in near field or far field regions. The resolution analysis of the imaging functional is analyzed where the explicit decay rate of the functional is established. A connection with the orthogonality sampling method by Potthast is also studied. The sampling method is then combined with a deep neural network to solve the inverse scattering problem. This combined method can be understood as a network using the image computed by the sampling method for the first layer and followed by the U-net architecture for the rest of the layers. The fast computation and the knowledge from the results of the sampling method help speed up the training of the network. The combination leads to a significant improvement in the reconstruction results initially obtained by the sampling method. The combined method is also able to invert some limited aperture experimental data without any additional transfer training.