Joint Inversion Method Based On Structural Similarity Constraints

The electromagnetic inverse scattering problem(also known as electromagnetic inversion/reconstruction)is an important research field in the study of electromagnetic theory.Due to its outstanding practical value,it has been widely used in many research fields such as earth remote sensing,biomedical imaging and ground object exploration.However,the nonlinear and ill-conditioned nature of electromagnetic(EM)inversion is a great challenge that hinders its development.With the rapid development of computational electromagnetics,its problems are expected to be improved,and new requirements for inversion quality are also put forward.Scholars no longer study the scattering of single physical field,but turn their attention to the joint inversion method of multiple physical fields.Joint inversion refers to using the correlation between multi-physics experimental data to constrain each other through appropriate rules,so that the final inversion results are closer to the actual model.Compared with the separate EM inversion,the joint inversion method can reduce the multi-solution problem in the inversion process on the basis of ensuring the inversion speed,thereby effectively solving its nonlinearity and improving the inversion performance.This thesis mainly focus on the joint inversion method of two-dimensional EM and acoustic.The main contents are as follows:First,this thesis introduces the basic theory of EM scattering and inverse scattering theory.On this basis,a more efficient inversion method—the subspace-based optimization method(SOM),is introduced,and the inversion steps of this method are given.And then,through simulation results analyzes the impacts of noise and regularization parameters on SOM.Secondly,on the basis of SOM,this thesis adds the cross gradient function to realize the joint inversion method based on the structural similarity constraint—the joint inversion method based on the cross gradient function(JSOM-CGF),and analyzes the effectiveness of the method through numerical examples.The main idea is to use the outer product gradient function in the objective function to constrain the acoustic speed in the acoustic inversion and the relative permittivity in the EM inversion,so as to achieve the purpose of improving the imaging quality of a single EM inversion.At the same time,a method of constraining EM inversion by using the structural prior information of acoustic inversion is proposed,that is,a joint inversion method based on spatial structure constraints(JSOM-SSC),and the validity of this method is verified by simulation.The core idea of the spatial structure constraint is the same as JSOM-CGF,both of which use the structural similarity of physical parameters between different physical fields.It is known that the image segmentation technology can quickly and accurately confirm the location information of the target from the background.Therefore,it is feasible to use it to extract the prior information of the spatial structure from the acoustic inversion,thus showing the huge advantage of JSOM-SSC.Finally,the content of this thesis is summarized,and the future prospect of the joint inversion method is put forward.