New Efficient 2-D Lattice Structures for General Autoregressive Modeling of Random Fields

In this paper, we present a new efficient general 2-D autoregressive (AR) lattice modeling technique of random fields. Our proposed approach is capable of simultaneously providing all possible types of 2-D causal quarter-plane (QP) and asymmetric half-plane (ASHP) AR models for an arbitrary rectangular shape of the prediction support region (PSR). It is shown that it is also possible to obtain various noncausal half-plane AR models without any additional computational cost. This new lattice structure introduces only one row or one column of new observation points into the existing rectangular PSR when the order of the model increases in the horizontal or vertical direction at each of the recursive order incrementation stage, respectively. Starting with a given random data field, a set of auxiliary forward and backward prediction error fields (PEFs) for the horizontal and vertical directions are generated. After recursive order updates to the desired size of the rectangular PSR, all types of causal QP/ASHP and noncausal half-plane 2-D lattice models are obtained by deriving the appropriate PEF from the remaining ones. In addition to developing the basic theory, the presentation includes the derivation of the synthesis model transfer functions from the calculated lattice parameters. It is shown that the proposed auxiliary horizontal and vertical backward prediction error filters inherently generates the mutually orthogonal realization vectors and thus are optimum for all stages. The theory has been confirmed by computer simulations.