Multiscale Bayesian Methods for Discrete Tomography

Statistical methods of discrete tomographic reconstruction pose new problems both in stochastic modeling to define an optimal reconstruction, and in optimization to find that reconstruction. Multiscale models have succeeded in improving representation of structure of varying scale in imagery, a chronic problem for common Markov random fields. This chapter shows that associated multiscale methods of optimization also avoid local minima of the log a posteriori probability better than single-resolution techniques. These methods are applied here to both segmentation/reconstruction of the unknown cross-sections, and estimation of unknown parameters represented by the discrete levels.