In this contribution we address the problem of reconstructing particulate media from limited morphological information that may be readily extracted from 2D images of their microstructure. Sixty-five backscatter SEM images of the microstructure of a lightly consolidated pack of glass spheres are analyzed to determine morphological descriptors, such as the pore-pore autocorrelation function and pore and solid phase chord distributions. This information is then used to constrain the stochastic reconstruction of the glass sphere packing in two dimensions using a simulated annealing method. The results obtained demonstrate that the solid-phase chord distribution contains additional information that is critical for the reconstruction of the morphology of particulate media exhibiting short-range order. We further confirm this finding by successfully reconstructing the microstructure of a pack of irregular silica particles.