2-DIMENSIONAL ORTHOGONAL LATTICE STRUCTURES FOR AUTOREGRESSIVE MODELING OF RANDOM-FIELDS

Two-dimensional orthogonal lattice filters are developed as a natural extension of the 1-D lattice parameter theory. The method offers a com plete solution for the Levinson-type algorithm to compute the predicti on error filter coefficients using lattice parameters from the given 2 -D augmented normal equations. The proposed theory can be used for the quarter-plane and asymmetric half-plane models. Depending on the inde xing scheme in the prediction region, it is shown that the final order backward prediction error may correspond to different quarter-plane m odels. In addition to developing the basic theory, the presentation in cludes several properties of this lattice model. Conditions for lattic e model stability and an efficient method for factoring the 2-D correl ation matrix are given. It is shown that the unended forward and backw ard prediction errors form orthogonal bases. A simple procedure for re duced complexity 2-D orthogonal lattice filters are presented. The pro posed 2-D lattice method is compared with other alternative structures both in terms of conceptual background and in terms of complexity. Ex amples are considered for the given covariance case.