Closed-Form Solution for the Reconstruction Problem in Porous Media

The statistical reconstruction of lattice models of real porous media is one of the basic engineering problems in the theory of porous structure and has a variety of applications in the study of transport, in mineral processing, and in material characterization. A systematic analysis of the reconstruction problem of porous media is presented, as well as a closed-form solution. The solution is presented in the form of a linear filter acting on Gaussian processes by means of a superposition of elementary correlated processes with prescribed correlation properties, and in the form of a memoryless process recalling the theory of Khinchin on the properties of correlation functions. The connection of this approach with models of correlated percolation is also discussed.