Complex-Valued Pix2pix-Deep Neural Network for Nonlinear Electromagnetic Inverse Scattering

Nonlinear electromagnetic inverse scattering is an imaging technique with quantitative reconstruction and high resolution. Compared with conventional tomography, it takes into account the more realistic interaction between the internal structure of the scene and the electromagnetic waves. However, there are still open issues and challenges due to its inherent strong non-linearity, ill-posedness and computational cost. To overcome these shortcomings, we apply an image translation network, named as Complex-Valued Pix2pix, on the inverse scattering problem of electromagnetic field. Complex-Valued Pix2pix includes two parts of Generator and Discriminator. The Generator employs a multi-layer complex valued convolutional neural network, while the Discriminator computes the maximum likelihoods between the original value and the reconstructed value from the aspects of the two parts of the complex: real part and imaginary part, respectively. The results show that the Complex-Valued Pix2pix can learn the mapping from the initial contrast to the real contrast in microwave imaging models. Moreover, due to the introduction of discriminator, Complex-Valued Pix2pix can capture more features of nonlinearity than traditional Convolutional Neural Network (CNN) by confrontation training. Therefore, without considering the time cost of training, Complex-Valued Pix2pix may be a more effective way to solve inverse scattering problems than other deep learning methods. The main improvement of this work lies in the realization of a Generative Adversarial Network (GAN) in the electromagnetic inverse scattering problem, adding a discriminator to the traditional Convolutional Neural Network (CNN) method to optimize network training. It has the prospect of outperforming conventional methods in terms of both the image quality and computational efficiency.