3-D Lattice predictive modeling of random fields

The theory of quarter-plane autoregressive (AR) lattice parameter modeling of two-dimensional (2-D) fields is extended to three-dimensional (3-D) case with cubic-space support involving seven lattice parameters and eight prediction error fields at each stage. The relationship between the cubic-space 3-D transfer function and lattice parameters, and the sufficient lattice parameter stability conditions are also presented. Numerical examples are included to verify the formulation.