  We report a multiscale approach of broad applicability to stochastic
reconstruction of multiphase materials, including porous ones. The approach
devised uses an optimization method, such as the simulated annealing (SA) and
the so-called entropic descriptors (EDs). For a binary pattern, they quantify
spatial inhomogeneity or statistical complexity at discrete length-scales. The
EDs extract dissimilar structural information to that given by two-point
correlation functions (CFs). Within the SA, we use an appropriate cost function
consisting of EDs or comprised of EDs and CFs. It was found that the stochastic
reconstruction is computationally efficient when we begin with a preliminary
synthetic configuration having in part desirable features.
  Another option is low-cost approximate reconstructing of the entire
multiphase medium beyond the SA technique. The information included in the
target ED-curve was utilized for this purpose. For a given volume fraction the
low-cost trial microstructures can be generated in two ways. In the first one,
applied to ceramics and carbonate samples, the interpenetrating spheres
generate a number of trial configurations. In the second one, with phase-EDs,
here used to the sandstone sample, the overlapping superspheres do it. Both
methods use a radius determined from the EDs-linked two-exponent power-law.
However, the supersphere deformation parameter allows controlling of the
spatial inhomogeneity of prototypical microstructures. At last, even for a
hypothetical ED-curve (under reasonable assumptions), the specific
microstructure can be found, if it is realizable for a given volume fraction.
In general, the EDs-based methods offer a compromise between computational
efficiency and the accuracy of reconstructions.
