Statistical reconstruction of two-phase random media

•A robust and efficient algorithm to reconstruct two-phase composites with random morphology.•The new method is based on an explicit nonlinear transformation of Gaussian random fields.•The new method is highly efficient and particularly suitable for large-scale reconstructions. A robust and efficient algorithm is proposed to reconstruct two-phase composite materials with random morphology, according to given samples or given statistical characteristics. The new method is based on nonlinear transformation of Gaussian random fields, where the correlation of the underlying Gaussian field is determined explicitly rather than through iterative methods. The reconstructed media can meet the binary-valued marginal probability distribution function and the two point correlation function of the reference media. The new method, whose main computation is completed using fast Fourier transform (FFT), is highly efficient and particularly suitable for reconstructing large size random media or a large number of samples. Its feasibility and performance are examined through a series of practical examples with comparisons to other state-of-the-art methods in random media reconstruction.