Research On Recovery Algorithms In Compressive Sensing And Its Appication In Computational Electromagnetics

Methods for computational electromagnetics(CEM)have been widely applied in electromagnetic field and microwave engineering.Following the development of electromagnetic theory and its applications,analysis of electrically large objects under multiple incident angles has run into the bottleneck of CEM.The thesis focus on the compressive sensing(CS)theory that is introduced in CEM recently,and the applications of CS to method of moments(MOM)and finite-element boundary-integral(FE-BI)method are also improved and optimized.The main work of the thesis can be summarized as:Firstly,the theory of CS is explained.And key techniques such as sparse representation,measurement matrix and recovery algorithms are studied.Especially,recovery algorithms including orthogonal matching pursuit(OMP),compressed sampling matching pursuit(CoSaMP),subspace pursuit(SP),sparse adaptive matching pursuit(SAMP)and generalized orthogonal matching pursuit(GOMP)are introduced in detail,and programming implementation and comparative analysis are also accomplished.Secondly,the application of CS to CEM is introduced based on the method of moments.An undetermined equation model and the new incident source over a wide angle are constructed by CS.Different recovery algorithms for CS are applied to solve the induced currents under the two proposed methods and the corresponding results are compared with each other,it is found that selection of recovery algorithms not only has important influence on the computational accuracy and efficiency by itself but also has more important influence on the total number of measurements.Based on comprehensive consideration,GOMP method are more suitable for the two computational models mentioned above.Finally,the combination of compressive sensing and FE-Bi is studied.The computational efficiency of using FE-BI method to solving electromagnetic problems over a wide incident angle is improved by the construction of a new incident source based on CS.Meanwhile,the computational accuracy and efficiency together with the total number of measurements for different recovery algorithms are also analyzed and optimized,and the total computational efficiency is improved by suitable selection of recovery algorithms.