Hierarchical sampling with constraints

Reconstruction of porous media images is required in order to study different properties of these material. Our research interest is on generating samples from the posterior model in which low resolution measurements are combined with a prior model. The reconstruction task becomes intractable when the size of the samples increases, since it is based on simulated annealing which is a slow convergence algorithm. The hierarchical approaches have been applied to tackle this problem, in the case of sampling from the prior model. However, in the posterior sampling case, defining a suitable measurement model at each scale still remains a challenging task. In this paper we define how we can incorporate the measurement in the hierarchical posterior model and then how we generate samples from that model.