TRUNCATED COSINE FOURIER SERIES EXPANSION METHOD FOR SOLVING 2-D INVERSE SCATTERING PROBLEMS

Truncated cosine Fourier series expansion method is applied for reconstruction of lossy and inhomogeneous 2-D media by using inverse scattering method in time domain. In this method, the unknown parameters are expanded in a cosine Fourier series and coefficients of this expansion are optimized in particle swarm optimization (PSO) routine with the aid of finite difference time domain (FDTD) method as an electromagnetic (EM) solver. The performance of the algorithm is studied for several 2-D permittivity and conductivity profile reconstruction cases. It is shown that since only a limited number of terms are retained in the expansion, using the proposed method guarantees the well-posedness of the problem and uniqueness of the solution and various types of regularization may be used to only have more precise reconstruction. It is also shown that the number of unknowns in optimization routine is reduced more than 75 percent as compared with conventional methods which leads to a considerable reduction in the amount of computations with negligible adverse effect on the precision of reconstruction. Sensitivity analysis of the suggested method to the number of expansion terms in the algorithm is studied, as well.