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

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.

A direct sampling-based deep learning approach for inverse medium scattering problems

“…We summarize the DSM-DL scheme in algorithm 1. The explicit loss function will be given in equation (35) in the numerical experiments. Specifically, if we discretize the index functions and the true contrasts on N d × N d grid points in Ω for 2D problems, then the input to the neural network is a tensor with the dimension N i × N d × N d , while the output of the neural network is a tensor with the dimension 1 × N d × N d , i.e.…”

“…The batch size is taken as 6 and we use a total of 30 epochs to train the neural networks. As we use the loss function (35), we actually have 6000 training data and the batch size is 12. The learning rate starts at 0.001 and decreases by a factor of 0.5 every 3 epochs.…”

“…Combining deep learning and sampling-type methods for solving inverse scattering problems was also studied recently in [35] by using the orthogonality sampling method. However, it only considered one incident wave and is mainly focused on recovering the shapes and locations of the scatterers.…”