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Solving Inverse Scattering Problems Based on Truncated Cosine Fourier and Cubic B-Spline Expansions

In this paper, a comparison between truncated cosine Fourier expansion (TCFE) and cubic B-spline expansion (CBSE) for representation of the unknown scatterer properties in solving inverse scattering problems is presented. In this comparison, the efficiency of both aforementioned expansion techniques is examined for permittivity and conductivity profile reconstruction problems. The study is carried out by converting the reconstruction problem to an optimization one and using the finite difference time domain (FDTD) method as forward electromagnetic (EM) solver and the differential evolution (DE) technique as global optimizer. The main benefit of the expansion representations of the unknown properties is the reduction of the ill-posedness, which is achieved by decreasing the number of unknowns of the inverse problem. The comparison is done under the same conditions of the number of population and optimization iterations. Numerical results related to the reconstruction of one-dimensional (1D) and two-dimensional (2D) scatterers indicate that both expansion methods are reliable tools for inverse scattering applications. It is shown that the use of the CBSE results in faster convergence of the reconstruction process compared to the TCFE. However, the TCFE gives more accurate reconstruction especially in the edges of scatterers. Both expansion techniques are robust against the presence of noise in the measurements.