A NOISE-TOLERANT SOLUTION TO THE MAGNETOSTATIC INVERSE PROBLEM FOR NONDESTRUCTIVE EVALUATION

We present a probabilistic analysis which, given a finite set of magnetic induction measurements, yields the ''most likely'' source current density. The need for a probabilistic analysis stems from the presence of noise in the measurements. In the noise-free limit, our algorithm reduces to the so-called minimum-norm estimate for the source current density. Our analysis differs from the work of previous investigators in its simplicity and completeness; the previous work drew substantially from measure theory and left the variance in a prior probability measure undetermined-whereas our analysis uses elementary probability theory and contains no free parameters. In numerical studies, we have applied our algorithm to the problem of identifying a crack at the edge of a thin metal plate. Simulating an impressed current in the plate, we computed the resulting magnetic induction and used our algorithm to obtain an estimated current density. Graphical images of the estimated current accurately reveal the position and size of the crack, and confirm that optimal estimates are obtained in the presence of noise.