Research On Electromagnetic Inversion Based On Compressed Sensing And Bayesian Theory

Electromagnetic inverse scattering can reconstruct the distribution of the detection targets' electrical parameters by using electromagnetic inverse algorithm,according to the detection data in the light of the propagation principle of electromagnetic wave,which has been widely used in biomedical imaging,nondestructive detection,remote sensing imaging and other fields.Electromagnetic inversion is a typical nonlinear and ill-conditioned problem.It is difficult to reconstruct the target effectively using traditional signal processing algorithms.Based on the linearized inverse scattering model,with Compressed Sensing(CS)and Bayesian Theory,this paper aims at the ill-conditioned problem of electromagnetic inversion and research on efficient electromagnetic inversion algorithms with higher noise immunity,faster calculation speed and stronger adaptability.The specific research contents are as follows:1.A linearized electromagnetic inverse scattering model is established from the point of view of mathematics and physics.In order to alleviate its ill-condition,considering the sparse nature of the target to be reconstructed,a sparse regularization method based on CS is introduced,which specifically includes Orthogonal Matching Pursuit(OMP)algorithm and Bayesian Compressed Sensing(BCS)algorithm.Besides,in order to solve the block target imaging problem with electromagnetic parameter piecewise constant properties,this paper uses Total Variational Comprehensive Sensing(TVCS)to solve norm minimization problem from the perspective of gradient domain sparseness,and then reconstructs the geometric features and electrical parameters of the target.The numerical simulation experiment verifies the advantages of electromagnetic inversion methods mentioned above.2.The application of gridless compressed sensing algorithm in electromagnetic inversion is studied.CS algorithm has been able to reconstruct high-resolution images with less computational cost.However,the discrete dictionary in traditional CS algorithm needs to be strictly matched with the real model,while it is hard to be achieved in practical applications.In order to solve this basicmismatch problem,a gridless compressed sensing algorithm based on the atomic norm minimization method is introduced and applied to Through-the-Wall Radar Imaging(TWRI).Finally,compared the algorithm inversion results with OMP and BP algorithms,which proves the superiority of this method.3.A hierarchical variational Bayesian inference(VBI)algorithm embedded with damping generalized approximate message passing(GAMP)is proposed.In electromagnetic inversion,since the detection target and the surrounding electromagnetic environment are often very complex,the performance of the traditional inversion algorithm will be seriously affected,because the sparse hypothesis can't be satisfied.To solve this problem,a hierarchical Gaussian mixture model is used to construct Bayesian prior model,and then VBI method based on maximum a posteriori probability estimation is used to make approximate estimation for each model parameter and hidden variables.In order to improve the operation speed,the damping GAMP algorithm is used to decouple the likelihood function in the probability model,and the VBI-GAMP algorithm is established.Through numerical simulation experiments in different electromagnetic inversion scenarios and comparison with TVCS results,the results show that the algorithm improves the inversion performance and provides a feasible method for electromagnetic inversion in complex environment.