Research And Application Of Numerical Methods Of 3D Electromagnetic Scattering Based On Compressive Sensing

With the development of modern technologies and the increasing military demand,radar imaging is of great significance in target recognization,detection and tracking.High-resolution inverse synthetic aperture radar(ISAR),which takes no-cooperative targets as research objects,plays an increasingly important role in feature extraction for targets.The research on ISAR techniques requires the measured data;however,it is quite difficult to obtain the data,and it will consume a large amount of manpower;material resources and time are even if it is feasible.Computational electromagnetics(CEM)technology has been greatly improved in recent years,which can supply simulation data for radar imaging research,so that expenses for modeling and real measured data for ISAR research are reduced greatly,thus contributing to the rapid improvement of real application systems.Morden radar targets usually works in high frequency.Based on electromagnetism theory,the target in high frequecy can be modeled as the sum of multipole scattering centers approximatively,and then the relavent information extracted from received data of scattering centers is used to caculate the features of the target inversely.In fact,radar imaging is to solve an inverse scattering problem.In recent years,many algorithms are promoted from the famous method of moment(MoM)based integral equation(IE)method,such as multilevel fast multipole algorithm(MLFMA)for large-scale targets EM problem or domain decomposition methods(DDM)for multi-scale complex targets EM problem.However,it remains an urgent problem to improve the efficiency of CEM algorithm for large-scale complex targets in the environment of a wide-incident angle,the complexity of iterative and repeated matrix calculation increases sharply.Nowadays,compressive sensing(CS)is popular in data processing and imaging areas.The CS theory breaks through the limits of Nyquist sampling theorm;it changes signal sampling into information sampling by adpoting the sparsity or compressibility of signals,and then constructs an incoherent measurement matrix with the transform basis to obtain a lower-dimention observed signal.Then,the reconstruction algorithm is used to recovery the original higher-dimention signal from the lower-dimention signal accurately with a high problility.The much fewer sampled signals are required by CS technique,so that the requirements for data transmission,processing and storage are reduced significantly.Therefore,CS theorm is researched and applied in many areas,such as digital signal,image processing,etc.It also attracts much attention in other areas.In this dissertation,CS technique is used with MLFMA or DDM to solve large-scale and multi-scale monostatic EM problems under incidents from a wide angle respectively.Moreover,information extracted from the received echo data is used for ISAR imaging.The complexity is highly reduced while maintaining the imaging resolution.Firstly,the basic theorem of EM equivanlence principle is reviewed and the basic principle and main steps of solving MoM are introduced.The basic theory of CS is outlined and three important technical indicators,i.e.the sparsity of signal,incoherent measurement matrix and recovery algorithms,are discussed in details.In order to solve EM scattering problems under incidents from a wide angle,on the basis of the sparsity of the signals from multiple angles,a compressed incident source with enough information but much fewer excitation waves is used with CS framework.For large-scale targets,CS theorm is used with MLFMA and the induced current is stimulated by the compressed incident excitation waves acting on the impendence matrix.A new measurement matrix is designed,which not only satisfies the restricted isometry property(RIP)restriction,but also greatly reduces the non-zero elements of the measurement matrix.Orthogonal matching pursuit(OMP),regulized OMP(ROMP),subspace pursuit(SP),sparsity adaptive matching pursuit(SAMP)are chosen to recover the original signals respectively.Considering the tradeoff of accuracy and efficiency,the common orthogonal matching pursuit(OMP)algorithm is finally chosen as the recovery algorithm in this paper.Numerical examples show that CS-MLFMA can not only recover the original signal accurately,but also improve the computational efficiency greatly.The signals with good sparsity in the transform domain can get improved computational efficiency up to 50%However,there are many multi-scale complex targets in practical engineering.The fast CEM algorithms cannot solve the problem of multi-scale complex targets for which the computation unknowns are greatly increased due to the non-uniform discrete scale while modeling for the whole object,which results in the extremely ill conditioned discrete matrix that makes the iteration cannot converge.Therefore,in this paper,for multi-scale complex targets in a wide angel,CS is proposed to be used with DDM.The current coefficients induced by the compressed sampling excitation waves in each sub-region can be used to recover the all-current coefficients induced by the excitation waves under the all incident anglesThe experimental results prove the accuracy of CS-DDM for EM scattering problem of the multi-scale complex targets.Simutaneously,the computational complexity is greatly reduced because of the reduction of the number of excitation waves in a wide angle.In addition,the complexity of the methods metioned in the paper is analyzed.It is shown that the efficiency of the computational complexity is mainly determined by the number of incident angles,measurement dimensions and the number of unknowns.Finally,the radar echo information extracted by CS-MLFMA and CS-DDM for large-scale and multi-scale complex targets located in high-frequency scattering region is used to successfully realize ISAR imaging by the traditional fast Fourier transform(FFT)method respectively.The compressed sampling data greatly reduces the complexity of signal acquisition,storage and processing while maintaining the imaging resolution,and the computational efficiency is greatly improved.