Research On Nonlinear Electromagnetic Inverse Scattering Method Based On Variational Framework

Electromagnetic inverse scattering can determine the spatial structure and electrical performance parameters of the target qualitatively and quantitatively by transmitting antenna into electromagnetic wave,according to the detection data of the antenna and the propagation principle of electromagnetic wave.It has been widely used in biomedical imaging,non-destructive detection,microwave imaging and other fields.Inversion of electromagnetic inverse scattering is a typical non-linear and illconditioned problem,which is usually solved by non-linear iterative optimization algorithm.In each iteration process,one or more forward problems are involved,which results in high computational cost.In view of the above problems,this paper studies the three aspects of electromagnetic field forward numerical calculation,nonlinear inverse scattering problem modeling based on variational framework and numerical optimization.The specific research contents are as follows:Firstly,based on the forward propagation model of electromagnetic wave and Lippmann-Schwinger equation,the bilinear equation of total field and scattered field data is constructed.The scattered field data are simulated by conjugate gradient method and fast iterative shrinkage threshold algorithm.By updating the total field and then solving the scattered field data,the implementation process of the two algorithms is given and the computational time cost is analyzed.Secondly,in the inversion process,through the variational framework,using the Alternating Direction Method of Multipliers(ADMM),a complex objective function is optimized into three linear sub-problems: contrast source,contrast and dual variables.The form of the solution.Introducing the augmented Lagrangian method to transform the constrained optimization problem into the extremum problem of the unconstrained objective function.The iterative process,algorithm framework and process of ADMM algorithm are expounded.The inversion reconstruction is carried out by using the simulated data and the measured data respectively,and the performance of the ADMM algorithm is verified from the aspects of inversion reconstruction effect,convergence speed and anti-noise performance.Finally,the ADMM algorithm is improved in both the reconstruction quality of the target scatterer and the convergence speed of the algorithm.The selection of penalty parameters in the traditional ADMM algorithm is generally based on empirical choices.The adaptive method is used to improve the selection of parameters,which can effectively improve the quality of inversion reconstruction of ADMM algorithm.In addition,a Fast-ADMM algorithm is proposed to improve the convergence speed of the algorithm.This method selects a better method for the selection of approximation function.The ADMM algorithm and Fast-ADMM are compared in terms of calculation time and convergence speed.