A new hybrid method that combining CS and FMM for multi-static scattering problems

In this paper, the compressive sensing (CS) is introduced into fast multipole method (FMM) for the purpose of reducing the angle sampling rate in solving multi-static scattering problems. The scattered fields induced by all excitations on one scattering angles are viewed as the proceeded signal, which is sparsely sampled by CS. Then the Huygens principle is introduced to convert the sparse sampling of the scattered fields to the measurements of the induced currents and the excitations. This results in a new multi-static scattering problem, which has much fewer excitations than that of the original one. And the FMM is introduced then to solve the new multi-static scattering problem. Finally, the orthogonal matching pursuit (OMP) algorithm is utilized to reconstruct the desired scattered fields. The validity and efficiency of the new CS-FMM method is derived by comparing with the traditional FMM method.