Research On Electromagnetic Inverse Scattering Methods Of Strong Dielectric Scatterers

The electromagnetic inverse scattering problems are inverse problems of reconstructing the position,shape and electrical properties of the scatterers through the incident electromagnetic field and the measured scattered electromagnetic field.The electromagnetic inverse scattering problems are strongly nonlinear and ill-conditioned.Due to the multiple scattering effects,when the scatterers have large electrical sizes and/or strong contrasts with the background,the nonlinearity will increase,which increases the difficulty of solving the inverse scattering problem.This kind of scatterer is recognized as a strong scatterer.The electromagnetic inverse scattering methods for reconstructing such scatterers have extensive and important applications in biomedical engineering,microwave remote sensing and non-destructive detection,etc.,and have been the focus of researchers in recent years.In this dissertation,aiming at the two dimensional strong dielectric scatterers,starting from the basic theory of electromagnetism,the main contributions are as follows:1.Hierarchical electromagnetic inverse scattering method for strong scatterers based on multi-frequency scattered fieldThe nonlinearity of the inverse scattering problem is related to the electrical size of the scatterer.If the frequency of the incident wave becomes higher,the electrical sizes of the scatterers become larger,and the nonlinearity of the inverse scattering problem becomes stronger,making it difficult to reconstruct the scatterers.If the frequency of the incident electromagnetic wave is reduced,although the nonlinearity of the inverse scattering problem is reduced,the resolution of the reconstruction result is also reduced.In this dissertation,a hierarchical subspace-based optimization method(HSOM)combines the subspace-based optimization method(SOM)and the hierarchical strategy is proposed.HSOM extracts the domain where the scatterer is located in the inversion at low frequencies,and the high-frequency inversion is only performed in this domain of the scatterer.Compared with frequency-hopping subspace-based optimization(FH-SOM),HSOM can obtain higher quality reconstructed images with less computation.2.Electromagnetic inverse scattering method for strong scatterers based on the joint inversion of electromagnetic and acoustic wavesScatterers have different properties in acoustic and electromagnetic fields.Many scatterers have high contrasts and strong nonlinearities in electromagnetic inversion.However,their contrasts are low in acoustic inversion and high-resolution imaging can be achieved.For such scatterers,this dissertation firstly proposed two joint inversion methods of acoustic and electromagnetic waves based on structural constraints for high-contrast and high-resolution imaging.Both methods are based on the framework of SOM.In the inversion process,one method is to use the cross gradient function to link the acoustic inversion and the electromagnetic inversion to reconstruct the objective function.The other method is to use the reconstruction results of acoustic inversion as the spatial structural constraints of the electromagnetic inversion process.And then a hybrid structural constraint method that combines the advantages of the first two methods is proposed.All three methods enable finer reconstruction of the structure and contrast of strong scatterers than the separated SOM.3.Electromagnetic inverse scattering method for strong scatterers based on iterative domain decomposition techniqueIn this dissertation,an iterative domain decomposition technique(IDDT)based on the SOM framework is proposed to reconstruct strong scatterers.IDDT-SOM takes advantage of the fact that different domains of the scatterers have different contributions to the scattered field.In the inversion process,the domain of interest is decomposed into the scatterer domain and the background domain firstly,and then the scatterer domain is decomposed into the dominant subdomain and the subordinate subdomain according to the contribution to the scatterer field.The objective function is reconstructed,and the electrical parameter distribution of the dominant subdomain is preferentially reconstructed,thereby reducing the dimension of the solution domain and reducing the nonlinearity of the inverse scattering problem.Then,the electrical parameter distribution of the entire scatterer domain is reconstructed by taking the electrical parameter distribution of the dominant subdomain as the initial information.This technique can be used repeatedly until a satisfactory reconstruction result is obtained.Compared with SOM,this method can reduce the nonlinearity of the inverse scattering problem and reconstruct stronger scatterers.In this dissertation,aiming at the strong dielectric scatterers,starting from its mathematical model and electromagnetic theory,using multi-frequency or multi-physical field information and iterative domain decomposition technique,a variety of electromagnetic inverse scattering methods are proposed,and the effectiveness of these methods is verified by numerical experiments,which provide a variety of technical paths for further research on strong dielectric scatterers inversion.