Microstructure reconstructions from 2-point statistics using phase-recovery algorithms

Two-point statistics describe the first-order spatial correlations between the constituent distinct local states in the internal structure of the material. These are usually recovered by randomly throwing vectors of all sizes and orientations into the material microstructure. Building on very recent advances in this emerging field, it is demonstrated in this paper that the complete set of 2-point correlations carry all of the information needed to uniquely reconstruct an eigen microstructure to within an translation and/or an inversion. For this purpose, novel algorithms based on phase-recovery methods used in signal processing have been developed and successfully implemented. The computational speed and the versatility of these new mathematical procedures are demonstrated through reconstruction of several two- and three-dimensional microstructures from their 2-point statistics.