Aiming at fast analysis of wide angle electromagnetic scattering problems, compressed sensing theory is introduced and applied, and a new kind of sparse representation of induced currents is constructed based on prior...Aiming at fast analysis of wide angle electromagnetic scattering problems, compressed sensing theory is introduced and applied, and a new kind of sparse representation of induced currents is constructed based on prior knowledge that originates from excitation vectors in method of moments. Using the new kind of sparse representation in conjugation with compressed sensing, one can recover unknown currents accurately with fewer measurements than some conventional sparse representations in mathematical sense. Hence, times of calculation by traditional method of moments used to obtain the required measurements can be reduced, which will improve the computational efficiency.展开更多
When compressed sensing is introduced into the moment method,a 3D electromagnetic scattering problem over a wide angle can be solved rapidly,and the selection of sparse basis has a direct influence on the performance ...When compressed sensing is introduced into the moment method,a 3D electromagnetic scattering problem over a wide angle can be solved rapidly,and the selection of sparse basis has a direct influence on the performance of this algorithm,especially the number of measurements.We set up five sparse transform matrices by discretization of five types of classical orthogonal polynomials,i.e.,Legendre,Chebyshev,the second kind of Chebyshev,Laguerre,and Hermite polynomials.Performances of the algorithm using these matrices are compared via numerical experiments,and the results show that some of them obviously work excellently and can accelerate wide angle scattering analysis greatly.展开更多
Under the theory structure of compressive sensing （CS）, an underdetermined equation is deduced for describing the discrete solution of the electromagnetic integral equation of body of revolution （BOR）, which will ...Under the theory structure of compressive sensing （CS）, an underdetermined equation is deduced for describing the discrete solution of the electromagnetic integral equation of body of revolution （BOR）, which will result in a small-scale impedance matrix. In the new linear equation system, the small-scale impedance matrix can be regarded as the measurement matrix in CS, while the excited vector is the measurement of unknown currents. Instead of solving dense full rank matrix equations by the iterative method, with suitable sparse representation, for unknown currents on the surface of BOR, the entire current can be accurately obtained by reconstructed algorithms in CS for small-scale undetermined equations. Numerical results show that the proposed method can greatly improve the computgtional efficiency and can decrease memory consumed.展开更多
基金Supported by the Key Project of Provincial Natural Science Research of University of Anhui Province of China under Grant No KJ2014A206, Anhui-Provincial Natural Science Foundation of China under Grant No 1408085QF104, the Key Project of the Ministry of Education of China under Grant No 212081, and the National Natural Science Foundation of China under Grant Nos 51477039 and 61301062.
文摘Aiming at fast analysis of wide angle electromagnetic scattering problems, compressed sensing theory is introduced and applied, and a new kind of sparse representation of induced currents is constructed based on prior knowledge that originates from excitation vectors in method of moments. Using the new kind of sparse representation in conjugation with compressed sensing, one can recover unknown currents accurately with fewer measurements than some conventional sparse representations in mathematical sense. Hence, times of calculation by traditional method of moments used to obtain the required measurements can be reduced, which will improve the computational efficiency.
基金Supported by the Key Program of National Natural Science Foundation of China under Grant No 60931002the National Natural Science Foundation of China under Grant Nos 61001033,61101064 and 51277001the Key Project of the Ministry of Education of China under Grant No 212081.
文摘When compressed sensing is introduced into the moment method,a 3D electromagnetic scattering problem over a wide angle can be solved rapidly,and the selection of sparse basis has a direct influence on the performance of this algorithm,especially the number of measurements.We set up five sparse transform matrices by discretization of five types of classical orthogonal polynomials,i.e.,Legendre,Chebyshev,the second kind of Chebyshev,Laguerre,and Hermite polynomials.Performances of the algorithm using these matrices are compared via numerical experiments,and the results show that some of them obviously work excellently and can accelerate wide angle scattering analysis greatly.
基金Supported by the National Natural Science Foundation of China under Grant Nos 51477039 and 51207041the Program of Hefei Normal University under Grant Nos 2014136KJA04 and 2015TD01the Key Project of Provincial Natural Science Research of University of Anhui Province of China under Grant No KJ2015A174
文摘Under the theory structure of compressive sensing （CS）, an underdetermined equation is deduced for describing the discrete solution of the electromagnetic integral equation of body of revolution （BOR）, which will result in a small-scale impedance matrix. In the new linear equation system, the small-scale impedance matrix can be regarded as the measurement matrix in CS, while the excited vector is the measurement of unknown currents. Instead of solving dense full rank matrix equations by the iterative method, with suitable sparse representation, for unknown currents on the surface of BOR, the entire current can be accurately obtained by reconstructed algorithms in CS for small-scale undetermined equations. Numerical results show that the proposed method can greatly improve the computgtional efficiency and can decrease memory consumed.
