Dual-Layer Compressive Sensing Scheme Incorporating Adaptive Cross Approximation Algorithm for Solving Monostatic Electromagnetic Scattering Problems

The compressive sensing technique can significantly improve the efficiency of the method of moments in solving the monostatic electromagnetic scattering problem by compressing the number of incident sources. However, in the case of extensive and dense angle sampling, the computational burden arising from the large size of the incident excitation matrix becomes a concern. In this paper, a dual-layer compressive sensing scheme incorporating the adaptive cross approximation (ACA) algorithm is proposed to further improve the efficiency of the compressive sensing-based method of moments (CS-MoM) for solving the monostatic electromagnetic scattering problem of three-dimensional objects. The proposed scheme is derived from hybridizing the new incident source-based CS-MoM and the overdetermined equation-based CS-MoM. Firstly, in the outer layer, the original incident sources are recombined to construct new incident sources. Then, in the inner layer, the overdetermined equation-based CS-MoM model is constructed to obtain the current coefficients for each new incident source. Finally, the current coefficients under the new incident sources are taken as measurement values for constructing an undetermined system in the outer layer, thus reconstructing the original current coefficients. In the proposed method, the original excitation matrix is extracted and then quickly filled into two smaller matrices by the ACA algorithm, which dramatically improves the efficiency of filling the excitation matrix. The proposed method significantly improves the computational efficiency, especially in filling the excitation matrix, compared to the unitary new incident source-based CS-MoM. Some simulation results are given to demonstrate the effectiveness and efficiency of the proposed method.