Shape reconstruction of metal pipes with corrosion defects using single frequency limited view scattered data

The inverse problem of reconstructing the cross sectional shape of a metal pipe from single frequency limited view electromagnetic scattered field data is considered. Specifically, the paper addresses the problem of assessing shape changes in the shadow region entailed by limited view data in 2D. 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 through iterations of a forward problem. A modified T-matrix method that exploits the use of FFT to speed up the computations is proposed for solving the forward problem. The proposed methodology is applied for shadow region shape change assessment to determine whether a metal pipe is corroded or not, and to reconstruct the shape of corrosion-like defect, over a range of size parameters. The study is carried out using Transverse Electric (TE) and Transverse Magnetic (TM) polarized fields. Numerical results of inversion using multi-objective optimization over a wide range of size parameter (ka  ) values show that errors in reconstruction are within 0.5% in the range of 1.4≤ka≤2.61.4≤ka≤2.6. Further, reconstruction with TE is found to lead to better reconstruction than with TM polarization. The effect of random noise in the scattered fields on shape reconstruction is also investigated.