DCT/DST and Gauss-Markov fields: conditions for equivalence

The correspondence addresses the intriguing question of which random models are equivalent to the discrete cosine transform (DCT) and discrete sine transform (DST). Common knowledge states that these transforms are asymptotically equivalent to first-order Gauss causal Markov random processes. We establish that the DCT and the DST are exactly equivalent to homogeneous one-dimensional (1-D) and two-dimensional (2-D) Gauss noncausal Markov random fields defined on finite lattices with appropriate boundary conditions.