EDDY-CURRENT TOMOGRAPHY USING A BINARY MARKOV MODEL

The non-destructive evaluation (NDE) problem we treat is the testing o f a globally homogeneous conductive medium for anomalies such as crack s and notches. The medium is illuminated with a monochromatic electric field; the anomalies induce eddy currents and they modify the total f ield which can be measured. The tomographic approach, aimed to draw up an image of the medium, is recent in this area. It corresponds to an extremely difficult ill-posed inverse problem and its resolution needs the use of pertinent prior information. The considered anomalies can be represented using images whose pixels can only take the values 0 an d 1. Our main contribution lies in the regularization of a large-suppo rt ill-posed observation operator using a locally constant binary imag e Markov random field. The resulting high-dimensional combinatorial op timization problem is tedious: neither exact resolution nor simulated annealing are feasible. Instead, we establish an equivalent continuous -valued optimization problem. A nearly optimal solution is then calcul ated using a graduated non-convexity algorithm adapted for this purpos e. The proposed inversion technique surpasses the particular NDE probl em and can be applied whenever a binary image is observed using a line ar system and corrupted by Gaussian noise.