Fast analysis of multi-static scattering problems with compressive sensing technique

- The CS together with FMM is introduced to the electromagnetic multi-static scattering problems.
- The scattered field generated by all excitations in one scattering angle is treated as the signal of interest.
- The FMM is applied as an electromagnetic solver to calculate the far zone scattered fields.
- The CS is utilized to decrease the number of times required to compute the matrix equations derived by FMM.

In this paper, the compressive sensing (CS) is introduced to the electromagnetic multi-static scattering problems for the purpose of reducing computation runtimes. During the simulations, the CS paradigm is worked as an incident angle reduction tool. The scattered fields generated by all excitations in one scattering angle are treated as the signal of interest, which is under sampled directly based on the CS theory. And then the measurement of the scattered fields is converted to the measurement of the induced currents and the excitations by the Huygens principle and the relationships between the induced currents and the excitations. By solving the measured matrix equation with the fast multipole method (FMM), one can get the measurement of the scattered fields. Finally, the orthogonal matching pursuit (OMP) is utilized to reconstruct the original scattered fields by solving an optimal ℓ1 norm equation. Numerical simulations demonstrate that, if the interpolation is not taken into account, the introduction of CS can save significantly while maintaining sufficient accuracy.