  Precise characterization of three-dimensional heterogeneous media is
indispensable in finding the relationships between structure and macroscopic
physical properties (permeability, conductivity, and others). The most widely
used experimental methods (electronic and optical microscopy) provide
high-resolution bi-dimensional images of the samples of interest. However, 3D
material inner microstructure registration is needed to apply numerous modeling
tools. Numerous research areas search for cheap and robust methods to obtain
"full" 3D information about the structure of the studied sample from its 2D
cuts. In this work, we develop a dynamic phase-retrieval stochastic
reconstruction algorithm that can create 3D replicas from 2D original images -
DDTF. The DDTF is free of artifacts characteristic of previously proposed
phase-retrieval techniques. While based on a two-point $S_2$ correlation
function, any correlation function or other morphological metrics can be
accounted for during the reconstruction, thus, paving the way to the
hybridization of different reconstruction techniques. In this work, we use
two-point probability and surface-surface functions for optimization. To test
DDTF, we performed reconstructions for three binary porous media samples of
different genesis: sandstone, carbonate, and ceramic. Based on computed
permeability and connectivity ($C_2$ and $L_2$ correlation functions), we have
shown that the proposed technique in terms of accuracy is comparable to the
classic simulated annealing-based reconstruction method but is computationally
very effective. Our findings open the possibility of utilizing DDTF to produce
fast or crude replicas further polished by other reconstruction techniques such
as simulated annealing or process-based methods.
