Compressed Sensing for Fast Analysis of Scatterring Problems With the use of Wavelet Expansions

A novel method which employs the recently developed theory of compressed sensing (CS) in method of moments (MoM) is presented. With a suitable discrete wavelet transform (DWT), the known impedance matrix, excitation and the unknown solution are localized, so the CS technique is introduced to construct the underdetermined equation that can be efficiently solved by the stagewise orthogonal matching pursuit technique (StOMP) method. Based on the fact of the significant correlation between the localized solution and excitation vector, the underdetermined equation can be constructed systematically and deterministically. Due to the computational complexity of StOMP depends not only on the size of equation, but also on the sparsity of solution, the computational cost of our method can be saved dramatically. The performance of the proposed approach is illustrated by numerical studies of electromagnetic field integral equations.