Eddy current testing of anomalies in conductive materials. II. Quantitative imaging via deterministic and stochastic inversion techniques

For pt.I, see ibid., vol.27, no.6, p.4416-37 (1991). Application of deterministic and stochastic quantitative inversion techniques to configurations similar to those treated in Pt.I by tomographic techniques is discussed. The defects are modeled as cylindrical inhomogeneities concealed within a homogeneous nonmagnetic metallic half-space. Values of the conductivity within the anomaly cross section have to be retrieved from multifrequency anomalous fields observed on a line above and parallel with the surface on the damaged block when a known time-harmonic source illuminates the block. Such quantitative imaging involves the ill-posed inversion of a Fredholm first-kind integral equation with exponentially damped kernel and requires some kind of regularization. In a deterministic context, an iterative algorithm provides a regularized generalized inverse, with the inconvenience that the stopping parameter should be appropriately chosen. In a stochastic context. Kalman filtering rapidly yields a good estimate of the conductivities, which could lead to a more precise but costlier solution