Shape reconstruction of corroded objects from limited view scattered data in frequency domain

Abstract

The problem of reconstructing the shape of a 2-D Perfect Electric Conductor (PEC) cylinder from limited view scattered near-field data is considered in the frequency domain. Firstly a modified T-matrix method is proposed for direct scattering problem, which uses the concept of 2-D analogue of T-matrix method to obtain the surface currents and Fast Fourier transforms to speed up the computations. Substantial enhancement in the computation speed is seen compared to the classical T-matrix method. The inverse scattering problem is formulated as a non-linear optimization problem that seeks to minimize the difference between measured data and the simulated data. The proposed inverse methodology is applied for (a) the determination of whether a cylinder is corroded or not, and (b) the shape reconstruction of corroded cylinder over a range of size parameters using Transverse Electric (TE) and Transverse Magnetic (TM) polarization. Synthetic data generated from commercial package (COMSOL) representing pulse-echo mode, of ground penetrating radar (GPR) experiment, is used in lieu of measured data. To exploit the information of scattered TE and TM fields, the inverse problem is formulated using multi-objective optimization. Numerical results over a wide range of size parameter (ka) values show that error in reconstruction are within 0.5% in the range of 1.2<ka<2.8. Further, reconstruction appears to be better with TE than TM polarization.