Research On Superresolution Methods Of Electromagnetic Inverse Scattering Reconstruction

Electromagnetic inverse scattering method is based on full wave electromagnetic calculation.Therefore,compared with other microwave imaging methods,inverse scattering reconstruction has a more accurate and universal physical model and a wider application prospect.Most of the current inverse scattering methods are applied to oil exploration,building interior perspective and breast cancer diagnosis imaging,which require low-frequency waves to penetrate obstacles.Therefore,the reconstruction target scale is mostly in the order of wavelength,which pose enormous challenges to imaging and reconstruction.In addition,when metallic and non-metallic materials are mixed in the imaging area,the reconstruction of the latter is easily disturbed by the former,which brings uncertainty to the quantitative reconstruction.Finally,in these complex scenes,the reconstruction method should be able to operate stably under the non-uniform background,which tests the robustness of the reconstruction method.Therefore,this dissertation mainly focuses on three challenges in the application of inverse scattering reconstruction:first,for the problem with mixed boundary conditions,an alternating parameter updating method is proposed to realize the accurate reconstruction of conductor and dielectric targets at the same time;Secondly,aiming at super-resolution,an super-resolution method based on superoscillation effect and material sparse a priori from the perspective of physical super-resolution and mathematical super-resolution is presented respectively;Thirdly,for the case of nonuniform background disturbance,the reconstruction strategy of partition optimization is given.Next,the four research contents for these three problems are introduced in detail:1.Inverse Scattering Method with Mixed Boundary ProblemWhen the scattering target is composed of conductor and dielectric objects,the skin effect of the conductor leads to an internal zero field,which results in the defects in the rank of the impedance matrix.Because the existence of conductor aggravates the ill-posedness of the inverse problem,the inverse scattering reconstruction of medium is seriously affected.To settle this problem,a mixed parameter model is proposed for the first time,which unifies the transmission coefficient of qualitatively boundary conditions and the contrast function of quantitative reconstruction in the same model.In order to deal with the ill-posedness influence of conductor in dielectric reconstruction,this dissertation innovatively proposes an alternating parameter updating method,which quantitatively reconstructs the dielectric contrast function and qualitatively reconstructs the conductor transmission coefficient alternately.Thus,in a single update,the dimension of the impedance matrix is reduced,the ill-posedness of the mixing boundary problem is alleviated,and the accurate reconstruction of the mixed target of conductor and medium is realized.The proposed method is verified on the simulation and measured data,and the reconstruction results are better than the reconstruction of their respective parameters.2.Super-Resolution Method based on Physical ModelUsually,the super-resolution imaging method based on the far-field model is difficult to exceed the limit resolution of the full aperture,that is,half a wavelength.However,the nonlinear inverse scattering method based on the accurate physical model has been verified many times to obtain the reconstruction accuracy of sub-wavelength order.Although most scholars qualitatively attribute it to the process of transforming evanescent wave into transmission wave in the model,there is a lack of quantitative inference,so there are many disputes about the theoretical interpretation of this superresolution ability.Based on the superoscillation theory,this dissertation gives the interpretation of nonlinear inverse scattering super-resolution reconstruction for the first time,and deduces the limit resolution of nonlinear inverse scattering reconstruction according to the relationship between superoscillation effect and signal-to-noise ratio.Because the total field of superoscillation can mix the high-frequency information of the target to the Green’s function passband through nonlinear procedure,the information can be compressed.Therefore,based on this theory,two incident field optimization methods are proposed,which can obtain reconstruction resolution less than half wavelength under a given signal-to-noise ratio.Furthermore,it is proved that this superresolution reconstruction method based on super oscillation effect is equivalent to the regularization process with preconditioner,which shows that the appropriate regularization method can improve the resolution of nonlinear inverse scattering reconstruction.The proposed method is verified by simulation and measured data,and the reconstruction effect is better than that of no superoscillation design.3.Super-Resolution Method based on A PrioriIll-posedness is the core of the inverse scattering problem,this paper reveals that the regularization with nonlinear effects can acquire super-resolution results.However,most of the existing sparse regularization methods are based on linear inverse problems,which are either not able to handle complex reconstruction targets or not able to solve nonlinear problems.Because most reconstruction targets consist of a limited variety of materials,two nonlinear regularization methods based on material sparsity are proposed in this dissertation.One method is to constrain the value sparsity of the solution through the value piking function.Another method is to design a multi-layer Bayes model to promote the sparsity of the solution,and realize the reconstruction by means of nonlinear inference.The proposed method is verified by simulation and measured data.Under the same conditions,the proposed method can obtain better reconstruction results than the existing nonlinear inverse scattering methods.4.Application of Super-resolution Methods with Nonuniform Background DisturbanceThe model of nonlinear inverse scattering reconstruction is based on the principle of volume equivalence,which equates the scatterer in the region of interest with the volume current in free space.In penetrating imaging problems such as through wall imaging or biomedical imaging,the non-uniform background needs to be reconstructed at the same time,which expands the reconstruction area and weakens the superoscillation effect.In this dissertation,a partition reconstruction strategy is proposed,which transforms the influence of other partitions into the background Green’s function while reconstructing the sub region,so as to simplify the amount of calculation,further optimize the superoscillation effect in the sub region and improve the reconstruction resolution.Simulation results verify the effectiveness of the proposed method.In conclusion,the three kinds of engineering problems are finally determined by the mathematical properties of the inverse scattering problem,that is,ill-posedness.Therefore,the foothold of all methods in this paper is the regularization theory,which provides a reference for the further study of inverse scattering reconstruction.