Research On Modeling And Inversion For Electromagnetic Inverse Scattering Problems

Electromagnetic inverse scattering problems(ISP)are concerned with reconstructing the spatial distribution of electrical performance parameters of dielectric objects in a domain of interest from the measurement of the scattered fields.Due to the inherent nonlinearity and ill-posedness of ISP,nonlinear iterative optimization methods are usually used to solve ISP.However,given the nature of iteration,these nonlinear iterative optimization methods usually involve a complex optimization problem with time-consuming imaging process so that it is difficult for these methods to provide imaging in real time with high performance.Meanwhile,some regularization parameters are artificially chose based on experience to alleviate the ill-posedness of ISP,but it lacks theoretical guidance on how to choose a proper and universal regularization function.In addition,owing to strong nonlinear fitting ability,the emerging deep learning techniques are especially suitable for solving inverse problems,which also have been widely applied in electromagnetic inverse scattering imaging field in recent years.Deep learning techniques can provide real-time imaging solutions,but it is difficult to incorporate the domain knowledge of inverse scattering.Furthermore,a high degree of nonlinearity and ill-posedness would reduce the generalization of deep learning.In order to tackle these above problems,this paper focuses on the numerical methods for electromagnetic forward scattering problem,the numerical optimization of non-learning iterative inversion methods,and the deeplearning-based inversion schemes.This paper also offers some insights on how to combine neural networks with the domain knowledge as well as traditional nonlearning techniques.The main work of this paper are summarized as follows:First,based on electromagnetic forward scattering model and electromagnetic field integral equation in free space,data equation and state equation are coupled.We construct the objective function of forward scattering problem,and numerically simulates the scattered field in the measurement domain by method of moments and frequency domain finite difference method,respectively.We analyze and compare the performance of the two methods in the simulated scenario and real scenario.Second,we design and implement three deep-learning-based inverse scattering inversion schemes: data-driven inverse scattering inversion scheme,deep-learningassisted optimization scheme and physical-model-inspired deep unrolling network scheme.We use the laws of physics and mathematics to design our required neural network architecture,and gradually incorporate the domain knowledge of inverse scattering and traditional non-learning imaging techniques into our required neural network.Moreover,we offer some corresponding insights based on three schemes.Finally,in the physical-model-driven nonlinear deep learning scheme,inspired by traditional iterative algorithms and existing neural networks,the inverse scattering inversion solution from traditional iterative optimization is transformed into a solution that integrates iterations into the deep network structure.By adding auxiliary variables,the original nonlinear problem is decomposed into several linear subproblems,and each iteration is mapped to the corresponding sub-module in the new network structure.This inversion scheme is able to generate quick and good imaging results.Its core idea is suitable for inverse scattering problems in any scenario(linear and nonlinear scenario).