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Regularized inversion of a distributed point source model for the reconstruction of defects in eddy current imaging

S. Bausson (SATIE, ENS Cachan, Cachan, France)
V. Thomas (SATIE, ENS Cachan, Cachan, France)
P.‐Y. Joubert (SATIE, ENS Cachan, Cachan, France)
L. Blanc‐Féraud (I3S, INRIA, Sophia‐Antipolis, France)
J. Darbon (CMLA, ENS Cachan, Cachan, France)
G. Aubert (Laboratoire Jean‐Alexandre Dieudonnée (JAD), CNRS: UMR6621 – Université de Nice Sophia‐Antipolis, Nice, France)



The inverse problem in the eddy current (EC) imaging of metallic parts is an ill‐posed problem. The purpose of the paper is to compare the performances of regularized algorithms to estimate the 3D geometry of a surface breaking defect.


The forward problem is solved using a mesh‐free semi‐analytical model, the distributed point source method, which allows EC data to be simulated according to the shape of the considered defect. The inverse problem is solved using two regularization methods, namely the Tikhonov (l2) and the 3D total variation (tv) methods, implemented with first‐ and second‐order algorithms. The inversion performances were evaluated in terms of both mean square error (MSE) and computation time, while considering additive white and colored noise, respectively, standing for acquisition errors and model errors.


In presence of colored noise, the authors found out that first‐ and second‐order methods provide approximately the same result according to the SEs obtained while estimating the defect voxels. Nevertheless, in comparison with (l2), the (tv) regularization was proved to decrease the MSE by 10 voxels, at the cost of less than twice the computational effort.


In this paper, an easy to implement mesh‐free model, based on virtual defect current sources, was used to generated EC data relative to a defect positioned at the surface of a metallic part. A 3D total variation regularization approach was used in combination with the proposed model, which appears to be well suited to the reconstruction of volumic defects.



Bausson, S., Thomas, V., Joubert, P.‐., Blanc‐Féraud, L., Darbon, J. and Aubert, G. (2011), "Regularized inversion of a distributed point source model for the reconstruction of defects in eddy current imaging", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 30 No. 6, pp. 1777-1791.



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