3-D reconstruction from a few radiographs using the metropolis dynamics with annealing

Abstract

We address the problem of reconstructing a piece-wise smooth 3-D distribution from a few 2-D integral projections. The stabilization of this ill-conditioned and underdetermined inverse problem is achieved via the introduction of a first order smoothness constraint which allows the recovery of discontinuities and leads to the minimization of a non-convex functional. In order to carry through this delicate optimization task, we resort to Metropolis-type annealing algorithms. In contrast to much of the work concerning annealing based inversion of ill-posed linear operators, we show that the performances of this class of algorithms can be markedly improved while not altering their theoretical convergence properties. Successful experiments about a non-destructive testing industrial application show significant benefits in terms of convergence speed as well as visual quality of the reconstruction results.