Radiographic Inspection of Thick Metal Components, Part II: a New Stochastic Approach to 3-D Reconstruction

We address the issue of reconstructing a piecewise constant 3D object from a few noisy projections in the radiographic inspection context described in Part I (Robini et al., 2006). The solution is defined as any global minimum of a discontinuous, highly multimodal cost function. To tackle this challenging optimization problem, we introduce a new class of hybrid algorithms which combines the theoretical advantages of simulated annealing with the practical advantages of deterministic continuation. We call this class of algorithms stochastic continuation (SC). SC inherits the convergence properties of generalized simulated annealing (under mild assumptions) and can be successfully applied to 3D reconstruction. Our numerical experiments indicate that SC outperforms simulated annealing and validate the model and methodology developed in Part I.