Research On Inversion Methods Of Dielectric Targets

The inverse problems of reconstructing dielectric objects are of great importance in academic research and practical applications.It has widespread applications in geoscience and biomedical imaging,etc.The main challenges of inverse problems originate in its inherent ill-posedness and nonlinearity.In this dissertation,the basic problem is separated from the practical applications.Based on the electromagnetic theories,the mathematical formulations are constructed.It is worth mentioning that this dissertation investigates the inverse problems of not only isotropic objects,but also uniaxial anisotropic objects.The dissertation mainly consists the following parts:1.Inverse problem of reconstruction of large uniaxial anisotropic objectsIn many practical applications,fine-resolution reconstructed images are required.In order to achieve finer resolution,higher frequency data must be used.However,the feasibility of the inversion methods will dramatically deteriorate when the electric size of the target increases,which leads to the failure of the inversion.Considering that the physical nature of uniaxial anisotropic objects is more complicated than isotropic objects,so are the inverse problems involving uniaxial anisotropic objects.To obtain the fine-resolution reconstruction results when dealing with large uniaxial anisotropic objects,we combined the frequency hopping and subspace-based optimization method(SOM).The proposed hybrid method is called FH-SOM(Frequency Hopping SOM).This hybrid method utilizes the results obtained at lower frequency to help the higher frequency inversion reduce the occurrence of local minima.Furthermore,this coarse inversion image provides a priori information for the reconstruction at higher frequencies to get finer resolution.Thus,although this method utilizes the data of multiple frequencies,the proposed method is still very efficient compared with single-frequency SOM(SF-SOM)in the point of view of computation time.2.Fast inversion methods based on SOMIn this dissertation,a diagonal approximation is introduced in the framework of SOM and the new method is named as Diagonal SOM(DSOM).This adopted diagonal approximation uses electric field determined by induced current in previous iteration to approximate total electric field inside investigation domain.Compared with SOM,DSOM has a more simplified objective function.Numerical examples demonstrate that the proposed DSOM provides reconstruction results that are comparable in quality to the ones obtained using SOM in high signal to noise ratio(SNR)background.Benefits from the diagonal approximation,the objective function of the inverse scattering problem becomes more simplified,giving rise to a significant computational saving.To mitigate the drawbacks of SOM,we proposed a new current construction method.By utilizing this new current construction method,it does not need to update the induced current by the basis functions of the noise subspace.The computational complexity of the singular value decomposition and inversion process are decreased significantly.This new kind of current construction method is combined with DSOM and the proposed method is called modified DSOM(MDSOM).Numerical examples demonstrate that MDSOM and DSOM has the same capability of reconstructing dielectric objects,but the computation time of MDSOM is far less than that of DSOM.Moreover,the proposed DSOM and MDSOM all have the capability of reconstructing uniaxial anisotropic objects.3.Solving inverse scattering problems in spatial frequency domainThe characteristics of the distribution of induced current in spatial frequency domain are investigated.It is concluded that the spatial frequency components of the induced current are concentrated at low frequencies in the circumstances that we concern.Based on the conclusion,we propose a current construction method by utilizing the basis functions of spatial frequency subdomain.The biggest advantage of the proposed current construction method is that the induced current is constrained in a smaller solution domain.We combine this current construction method with contrast source inversion method(CSI),and proposed method is called spatial frequency subdomain CSI(SFS-CSI).The SFSCSI is demonstrated its effectiveness and efficiency by not only numerical simulations but also experimental data.Compared with CSI,the proposed SFS-CSI has a significant decrease in computational loads.Meanwhile,we also combine SOM with the new current construction method and the method is called SFS-SOM.The same as the conclusion obtained in the SFS-CSI section,the SFS-SOM are more efficient than SOM in computation time.The proposed current construction method is capable of not only reconstructing isotropic objects,but also uniaxial anisotropic objects.In this dissertation,the inverse problems of reconstructing not only isotropic objects but also uniaxial anisotropic objects are investigated.Based on the analysis of the physical problem and the mathematical model,several new inversion methods are proposed.We demonstrate the effectiveness and the efficiency of the proposed methods by numerical simulations.The conclusions concluded in this dissertation can be a reference for further studies and related researches.