Research On Nonlinear Electromagnetic Inversion Method Based On Bayesian Theory

Electromagnetic inverse scattering imaging is a novel imaging technology based on electromagnetic induction.It emits incident electromagnetic waves to the investigation area and uses an inversion algorithm to process the electromagnetic echo signals scattered by the target in the investigation area to obtain the electromagnetic parameter distribution of the target.The electromagnetic inverse scattering problem is essentially an inversion problem,which is nonlinear and ill-posed,and it is difficult for traditional signal processing algorithms to effectively reconstruct high-contrast targets.Aiming at this problem,combined with Bayesian theory,this paper studies a nonlinear electromagnetic inversion algorithm with high imaging accuracy,strong anti-noise ability,and stable adaptability.The main research contents are as follows:1.Firstly,from a physical point of view,a mathematical model describing the electromagnetic scattering process is established,which is expressed as a rectangular equation;in order to solve its nonlinear problem,a Born Approximation(BA)method is introduced to convert the nonlinear equation into a linear equation;To solve its ill-posed problem,a regularization method based on Compressed Sensing(CS)is adopted,including: Orthogonal Matching Pursuit(OMP),Bayesian Compressed Sensing(BCS)and Total Variation Bayesian Compressed Sensing(TVCS)algorithm;finally,through numerical simulation experiments,the inversion of sparse and block targets with high and low contrast is realized respectively,and the feasibility of the above algorithms is verified.2.For the inversion of high-contrast sparse targets,this paper proposes a multi-task(MT)electromagnetic inversion algorithm with strong robustness and good inversion accuracy.In order to solve its nonlinear problem,a contrast source method is introduced,and the geometric characteristics and electrical parameters of the target are reconstructed by inverting the contrast source distribution;to solve its ill-posed problem,a regularization method based on Bayesian theory is adopted,specifically: Construct a Cluster Structured Sparsity(Clu SS)prior model suitable for multi-task inversion,improve reconstruction accuracy by sharing hidden control variables in parallel inversion tasks,and then use Variational Bayesian(VB)estimation to obtain the value of the unknown;by setting up simulation experiments,the proposed MT-Cluss-VB method was compared with the imaging results of other reconstruction algorithms,and the inversion results under different SNR and different sampling rates were quantitatively analyzed,so as to verify its imaging performance and anti-noise ability.3.For the inversion of high-contrast block objects,this paper proposes an electromagnetic inversion algorithm suitable for non-uniform block objects.First,a new Born Iteration(BI)method is used to solve the nonlinear problem.The total field and the target contrast are updated to the real value.At the same time,matrix operation is used to replace the full wave simulation in the update of the total field,so that the calculation speed is faster than the traditional BI method;then,use the Bayesian estimation theory to solve the ill-posed problem,specifically: constructing a Gaussian Mixture Model(GMM)to describe the block target prior information,The Generalized Approximate Message Passing(GAMP)algorithm is used to decouple the likelihood function in the probability model to improve the operation speed.Finally,through numerical simulation experiments,the results of the proposed BI-GMM-GAMP algorithm are compared with those of other inversion algorithms in different target scenarios.The results show that the proposed algorithm can reconstruct the shape and electromagnetic parameter distribution of high-contrast segmented targets more effectively.