An Enhanced Method for Inverse Scattering Problems Using Fourier Series Expansion in Conjunction With FDTD and Pso

Abstract

Abstract-A new computationally efficient algorithm for reconstruction of lossy and inhomogeneous 1-D media by using inverse scattering method in time domain is proposed. In this algorithm, cosine Fourier series expansion is utilized in conjunction with finite difference time domain (FDTD) and particle swarm optimization (PSO) methods. The performance of the proposed algorithm is studied for several 1-D permittivity and conductivity profile reconstruction cases. Various types of regularization terms are examined and compared with each other in the presented method. It is shown that the number of unknowns in optimization routine is reduced to about 1/3 as compared with conventional methods which leads to a considerable reduction in the amount of computations, while the precision of the solutions would not be affected significantly. Another advantage of the proposed expansion method is that, since only a limited number of terms are taken in the expansion, the divergence of the algorithm is far less likely to occur. Sensitivity analysis of the suggested method to the number of expansion terms in the algorithm is studied, as well.

Two-Dimensional Microwave Tomographic Algorithm for Radar Imaging Through Multilayered Media

“…In [9][10][11] the reconstruction of the target permittivity distribution is cast as the minimization of a non-quadratic cost function and solved with global or deterministic optimization methods. To improve the computation efficiency, the distorted Born iterative method (DBIM) and Born iterative method (BIM) dealing with intermediate scatterers are developed in [12,13].…”

Time Domain Inverse Scattering of a Two-Dimensional Homogenous Dielectric Object With Arbitrary Shape by Particle Swarm Optimization

“…It is a kind of swarm intelligence that is based on social behavior. In recent year, some researchers have focused on applying PSO in the inverse problem [31][32][33][34][35]. To the best of our knowledge, there is still no investigation on using the PSO to reconstruct the electromagnetic imaging of homogeneous dielectric cylinders with arbitrary shape in free space under time domain.…”

Microwave Imaging Within the Interval Analysis Framework

“…To investigate on the robustness of the IA-based inversion to noisy data, the reconstruction of the same scatterer profile of the previous example has been performed by varying the noise level within the range SN R = [5,50] [dB]. As indicated by the amount of the error indexes in Fig.…”

“…In order to avoid nonuniqueness and instability as well as to prevent the retrieval of false solutions [28], several inversion strategies have been proposed based on (a) a suitable definition of the integral equations either in exact [29,30] or approximated [31][32][33][34][35] forms to model the scattering phenomena, (b) the exploitation of the available a-priori information on some features of the scenario/scatterers under test [15,[36][37][38][39] or/and the knowledge of input-output samples of data and reference solutions [40][41][42] and/or the information acquired during the inversion process [43][44][45][46][47], and (c) the use of suitable global optimization strategies [48][49][50][51][52][53][54][55]. Whatever the approach, inversion methods generally consider an optimization step aimed at minimizing/maximizing a suitably defined data-mismatch cost function through gradient or evolutionarybased algorithms with still not fully resolved drawbacks.…”