Research On Accurate Imaging Techniques Of High-resolution Electromagnetic Inverse Scattering

Electromagnetic inverse scattering imaging is a kind of inverse problem,whose inherent ill-posedness and nonlinearity poses great challenges to high-quality reconstruction of target.Since the available information about target is limited in practical scenario,it is rather difficult to achieve accurate reconstruction.Therefore,it is of great significance to study the high-resolution accurate imaging technology.In this dissertation,we focus on three aspects: First,since the existing inversion algorithms fail to study thoroughly the super-resolution mechanism,we propose a super-resolution imaging method based on orbital-angular-momentum(OAM)waves,where the physical mechanism of super resolution is analyzed in detail.Second,to the best knowledge of the author,there are no accurate imaging techniques for inverse scattering problems yet,and we have proposed an accurate recovering algorithm based on joint-sparse reconstruction.Third,to overcome the noise disturbance,we have presented a high-quality imaging algorithm based on liner sampling method(LSM)and weighted differential evolution(DE)algorithm,and recovery of buried targets in half-space model is demonstrated to validate the method.Specifically,this dissertation mainly conducts the research from the following aspects.Firstly,the electromagnetic inverse scattering imaging model in free space is established,which lays a foundation for further research on imaging algorithms.From a mathematical point of view,the difficulties of solving the problem of electromagnetic inversion are analyzed,namely non-posedness and nonlinearity.Then,several classical inversion techniques,mainly categorized by the linear method and the nonlinear method,are introduced.The classic contrast source inversion(CSI)method and linear sampling method are emphasized and analyzed in detail,and the two algorithms are verified by numerical simulation.The effectiveness of CSI and LSM lays the foundation for following research.Secondly,the CG-FFT(conjugate gradient fast Fourier transform)method for solving the forward problem is analyzed in detail.The electromagnetic inverse scattering problem usually consists of forward problem and inverse problem.On the one hand,in order to test imaging algorithms,the forward algorithm is employed to generate scattering data;on the other hand,some imaging algorithms also involve solving the forward problem.Therefore,it is also of great significance to research on methods for solving forward problems.Starting from the integral equation,we have analyzed the discretization process of the model,and the FFT calculation format are discussed in detail.Then the conjugate gradient iterative algorithm is introduced.Numerical simulation demonstrates the effectiveness of the algorithm.Thirdly,since the realizable resolution in the existing imaging algorithms is limited,we have proposed a super-resolution technique based on OAM electromagnetic wave.A method of generating OAM electromagnetic wave in two-dimensional case is proposed and the mechanism of super-resolution under illumination by OAM electromagnetic wave is analyzed.It is found that due to the interesting characteristics of OAM electromagnetic wave,when it is used as the incident field,the evanescent wave information of the target can be converted into propagating wave.The converted information makes the far-field measurement data contain a wide spectrum of information,which can improve the imaging resolution.Besides,we have found that,in the super-resolution imaging algorithm,on the one hand,it is necessary to convert more evanescent wave information about the target into the propagating wave,and on the other hand,it is necessary to make full use of the evanescent wave information,that is,to extract the evanescent wave information from the scattered field data.The conclusion provides a reference for the research of super-resolution imaging algorithms.Finally,the OAM super-resolution technique is combined with the CSI method,and an OAM-CSI method is proposed.In the OAM-CSI method,we first reconstruct the contrast function directly,by which the evanescent wave information is preserved,and subsequently the CSI method proceeds with the contrast function being initial value,thus,the super-resolution imaging of the target is realized.Fourthly,in order to achieve accurate imaging,an accurate imaging method based on joint sparse theory is proposed.Since the compressive sensing model is linear while the inverse scattering problem is nonlinear,the contrast source is defined to build the linear relationship with the scattering fields,which enables us to apply compressive sensing theory to the inverse scattering problem.In order to use the correlated information between contrast sources under different illuminations,a multiple measurement vectors(MMV)model is constructed,and we use a hybrid-norm method to reconstruct the contrast sources.Considering that the support set of the contrast source is identical to that of contrast function,we can define the targets support from the reconstructed contrast sources.Since the accurate position information of the target is strong a priori information,we encode the position information into a binary mask,and add the mask into the CSI method to form a mask-beneficial CSI method.If the mask information is accurate,the perfect reconstruction of the target can be achieved.Finally,to realize accurate recovery with noise-corrupted data,we have studied the inversion of buried targets in half-space scenario,and have proposed a high-quality imaging algorithm based on LSM and weighted DE.To build the inverse scattering model in half space,we firstly derive the two-dimension Green's function in planar layered media,and applying CG-FFT method for solving the forward problem.For layered-media case,the relationship between the variables has both convolution and correlation format,and we modify the FFT matrix to make it appropriate for applying FFT fast calculations.As to the high-precision reconstruction algorithm,robustness of LSM is employed to roughly estimate the target support set.Based on the LSM results,we employ the DE algorithm to further optimize the support and find the support set that best matches the actual position.When implementing the DE algorithm,considering the magnitude of the indicator function of the LSM solution corresponds to the probability that the position belongs to the real target,the crossover probability for different elements in the DE gene are optimized,which accelerates the convergence of the algorithm.Using the optimal mask searched by DE,combined with the CSI method,high-precision reconstruction of buried targets can be achieved.To sum up,in this dissertation,the OAM-based super-resolution technique and precise reconstruction algorithms are proposed,which may provide reference for further research on electromagnetic inverse scattering problem.