Two-dimensional orthogonal lattice structures for autoregressive modeling of random fields


Kayran A. H.

IEEE TRANSACTIONS ON SIGNAL PROCESSING, vol.44, no.4, pp.963-978, 1996 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 4
  • Publication Date: 1996
  • Doi Number: 10.1109/78.492548
  • Journal Name: IEEE TRANSACTIONS ON SIGNAL PROCESSING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.963-978
  • Istanbul Technical University Affiliated: Yes

Abstract

Two-dimensional orthogonal lattice filters are developed as a natural extension of the 1-D lattice parameter theory. The method offers a complete solution for the Levinson-type algorithm to compute the prediction 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 indexing scheme in the prediction region, it is shown that the final order backward prediction error may correspond to different quarter-plane models. In addition to developing the basic theory, the presentation includes several properties of this lattice model. Conditions for lattice model stability and an efficient method for factoring the 2-D correlation matrix are given. It is shown that the unended forward and backward prediction errors form orthogonal bases. A simple procedure for reduced complexity 2-D orthogonal lattice filters are presented. The proposed 2-D lattice method is compared with other alternative structures both in terms of conceptual background and in terms of complexity. Examples are considered for the given covariance case.