One-dimensional profile reconstruction using cosine Fourier and cubic B-spline expansions

In this paper, truncated cosine Fourier expansion (TCFE) and cubic B-spline expansion (CBSE) techniques are used for solving one-dimensional (1-D) inverse scattering problems. Finite difference time domain (FDTD) and differential evolution (DE) methods are hired as forward solver and global optimizer, respectively and performance of the expansion methods is studied and compared in terms of reconstruction accuracy and convergence rate for permittivity and conductivity profiles reconstruction. It is shown that although both methods are powerful tools in solving inverse scattering problems with the main features of reduction the number of unknowns and removal the need to regularization term in comparison with conventional pulse function expansion (PFE) method, CBSE has the winning factors of controllable coefficients and the better ability of reconstruction the sharp edges.