Research On Theory And Method Of Full-Wave Electromagnetic Imaging

The electromagnetic inverse scattering problem(ISP)is designed to reconstruct the geometric shape,constitutive parameters of the unknown scatterers by using the measured scattered field data outside the domain of interest(Do I).It has been widely used in biomedical imaging,target recognition,non-destructive testing,microwave remote sensing,and so on.Due to the ill-posedness and nonlinearity of the ISP,some existing imaging methods are faced with problems such as low imaging accuracy,slow imaging speed,and inability to reconstruct scatterers with electrically large dimensions or high contrast.In response to the above problems,this thesis set out to study how to effectively reduce the nonlinearity of the ISP,how to establish imaging algorithms by using the phaseless-data,and how to combine qualitative and quantitative imaging algorithms to achieve realtime quantitative microwave imaging.Firstly,this thesis analyzes the origin of the nonlinearity in the ISP from the traditional LippmannSchwinger integral equations(LSIE)and then proposes the new contraction integral equations to establish the inversion model(denoted as contraction integral equations for inversion,CIE-I).Through the adjustable parameter, to effectively suppress the global nonlinearity introduced by the multiple scattering effects(MSE)inside the scatterer to reduce the nonlinearity of the ISP.In order to solve the instability in solving the contrast function due to the increase of nonlinearity of localeffect,two regularization techniques,namely a fast Fourier transform twofold subspace-based optimization method(FFT-TSOM)and the wavelet transform twofold subspace-based optimization method(WT-TSOM)are proposed to stabilize the CIE-I model in this thesis.With the aid of these two regularization schemes,the imaging algorithms based on the CIE-I model can effectively reduce the nonlinearity of the ISP,and successfully solve the highly nonlinear ISP.Secondly,in order to solve the problems of difficulty and inaccuracy of phase measurement,this thesis proposes to use the amplitude data of the total field to solve ISP.Based on the original data equation and state equation of the CIE-I model,a new intensity equation about the amplitude of total field is added,and these three equations are used to establish the basic inversion model with phaseless-data.In order to stabilize the CIE-I model,FFT-TSOM regularization technology is used to constrain the current space in a smaller subspace,and a multi-round nested optimization method is used to achieve the reconstruction of the target,which can effectively deal with strong scatterers(the ones with electrically large dimensions and /or high contrast).Finally,a hybrid input scheme(one that combines the qualitative and quantitative results)is proposed in this thesis to train deep neural networks(DNNs)to achieve real-time quantitative imaging of targets.The spatial information provided by the qualitative inversion algorithm,i.e.,direct sampling method(DSM),is introduced into the quantitative results obtained by the quantitative inversion algorithm,i.e.,Back-propagation(BP),and the quantitative results can be optimized.The optimized results are used as the inputs of the U-net to train the neural network.Compared with the BP-only input scheme,the trained network has better imaging quality,and the DSM only involves the inner product operation,which hardly increases the additional computational burden.