A novel electromagnetic tomography reconstruction method based on Radial Basis Functions for defect detection

Electromagnetic tomography (EMT) is a widely utilized technique for non-destructive defect imaging. However, the inverse problem in EMT is inherently ill-posed due to the limited number of coils in EMT arrays relative to the extensive mesh cells required for representing the sensing field. This ill-posedness complicates defect reconstruction and can lead to inaccuracies, including false positives or missed detections. Leveraging the characteristic smooth distribution of defect-induced electromagnetic response profiles, we propose a novel iterative reconstruction method based on radial basis functions (RBF). This approach represents the defect distribution within the imaging domain using a series of RBF functions, transforming the original relative conductivity reconstruction problem into the estimation of RBF coefficients. By substantially reducing the number of unknowns and exploiting the superior defect approximation capabilities of RBFs, the proposed method achieves improved defect reconstruction performance compared to conventional techniques, while also demonstrating accelerated reconstruction speed. The Sigmoid RBF demonstrates the best reconstruction performance among all methods, with an average reconstruction error of 0.01960 and a correlation coefficient of 0.7558. Wheras the best traditional method used can only reach 0.03506 and 0.4688, respectively. Furthermore, in conjunction with the proposed defect localization and sizing methodology, the reconstruction algorithm exhibits accurate defect positioning and size estimation capabilities, achieving an average defect localization error of 0.97 mm and an average defect area estimation error of 2.609 mm².