Markov chain monte carlo defect identification in nde images

We derive a hierarchical Bayesian method for identifying elliptically-shaped regions with elevated signal levels in NDE images. We adopt a simple elliptical parametric model for the shape of the defect region and assume that the defect signals within this region are random following a truncated Gaussian distribution. Our truncated-Gaussian model ensures that the signals within the defect region are higher than the baseline level corresponding to the noise-only case. We derive a closed-form expression for the kernel of the posterior probability distribution of the location, shape, and defect-signal distribution parameters (model parameters). This result is then used to develop Markov chain Monte Carlo (MCMC) algorithms for simulating from the posterior distributions of the model parameters and defect signals. Our MCMC algorithms are applied sequentially to identify multiple potential defect regions. For each potential defect, we construct Bayesian confidence regions for the estimated parameters. Estimated Bayes factors are utilized to rank potential defects (discovered by our sequential scheme) according to goodness of fit. The performance of the proposed methods is demonstrated on experimental ultrasonic C-scan data from an inspection of a cylindrical titanium billet.