Mapping defects in a conductive half-space by simulated annealing with connectivity and size as constraints

In a wave framework, eddy current nondestructive evaluation of a void defect in a conductive half-space is attempted from aspect-limited, frequency-diverse data. As a first step a linearized version of this non-linear, ill-posed inversion problem is considered. The test zone is modeled as a distribution of cells either black (void) or white (metal)- an inclusion of known, constant conductivity could be considered similarly. The optimal distribution is such that the minimum of a cost function made of the quadratic difference between data and replica fields plus two regularization terms, one linked to the size of the defect, the other to its connectivity, is reached. A simulated annealing algorithm is used to do so. Salient features of the evaluation procedure are illustrated by examples from both noiseless and noisy synthetic data, in particular the fact that the connectivity constraint results in a faster retrieval of a more "compact" anomaly.