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Closed interface shape characterization methods based on wavelet transform

Inclusion detection problems are widespread in industrial production processes. Electrical resistance tomography (ERT) is a non-intrusive technology to image the conductivity distribution inside a closed pipeline from the electrical measurements at its boundary. Due to the advantages of high speed, high safety and low cost, it is promising for solving the inclusion problems. However, due to the ill-posed and non-linear character of ERT, its spatial resolution is low. Shape inverse problem uses the piecewise constant conductivity as a prior information and directly estimates the geometric configuration of the boundary of the inclusion. Comparing with the pixel based methods, there are much less unknowns in the shape based approaches and the results can be directly used for the quantitative analysis. As a crucial factor in shape inverse methods, parameterization of the target boundary will directly influence the reconstruction performance. In the paper, the wavelet transform is used to decompose the inclusion boundary based on its different time-frequency characteristics, and the Levenberg-Marquardt (L-M) method is used to search the optimal shape estimation. Numerical simulations show that the proposed shape reconstruction method has high accuracy and high convergence, and it is also robustness to the inclusion boundaries with sharp corners.