Sparse Transform Matrices and Their Application in the Calculation of Electromagnetic Scattering Problems

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.