Application Of Compressed Sensing Based On Priori-Knowledge To The Method Of Moments

In the electromagnetic theory and its engineering applications, the research of electromagnetic scattering mechanism has important practical significance. In addition to field testing, computational electromagnetics (CEM) is an effective tool in the study of the electromagnetic scattering characteristics. In CEM, the method of moments (MOM) has become one of the most main numerical methods due to its high precision and high efficiency. However, when the method of moments is used to solve problems of electromagnetics scattering over a wide incident angle, except for the computation point by point, and some interpolation approximation method, there is no any effective methods.To solving this problem, compressive sensing theory that developed in signal processing area recently is introduced and is used combined with the method of moments. Meanwhile, based on prior knowledge extracted form the excitation vector, a new method is formed to analyze wide angle scattering problems efficiently. The main work of the paper can be described as follows:Firstly, the discretized formulations of the method of moments and its fast algorithm are derived in detail, and these discretized formulations are also tested by program. Meanwhile, different numerical experiments are discussed to verify the algorithm.Secondly, the theoretical framework of two kinds of compressed sensing (CS) techniques is described, and the physical meaning of related concepts is explained. Three vital segments in compressed sensing, measurement matrix, sparse transform and reconstruction algorithm are discussed in detail. Furthermore, combined with the method of moments, the CS technique is used to construct a new algorithm for analyzing scattering problems over a wide incident angle. Several specific examples are presented and discussed. Meanwhile, a new sparse measurement matrix is constructed based on introduction of random sampling technique, the efficiency of measurement is also improved.Finally, the characteristic of impedance matrix equation formed by MOM is analyzed, and Taylor series expansion and binomial theorem are used to process the excitation vector so that some useful prior knowledge of the induced current is extracted to form a new sparse representation. Numerical analysis of differently shaped objects is proposed, and it is shown that the number of measurements is reduced drastically by the application of the new sparse representation under the condition that the reconstruction precision is maintained. Therefore, the efficiency of CS with the new sparse representation is greatly improved, which paves a good way for the engineering applications of CS combined with MOM.