Optimum quarter-plane autoregressive modeling of 2-D fields using four-field lattice approach

Kayran A. H., Parker S.

IEEE TRANSACTIONS ON SIGNAL PROCESSING, vol.45, no.9, pp.2363-2373, 1997 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 9
  • Publication Date: 1997
  • Doi Number: 10.1109/78.622958
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2363-2373
  • Istanbul Technical University Affiliated: Yes


A new orthogonal four-field two-dimensional (2-D) quarter-plane lattice structure with a complete set of reflection coefficients is developed by employing appropriately defined auxiliary prediction errors, This work is the generalization of the three-parameter lattice filter proposed by Parker and Kayran, After the first stage, four auxiliary forward and four auxiliary backward prediction errors are generated in order to obtain a growing number of 2-D reflection coefficients at successive stages. The theory has been proven by using a geometrical formulation based on the mathematical concepts of vector space, orthogonal projection, and subspace decomposition, It is shown that all four quarter-plane filters are orthogonal and thus optimum for all stages, In addition to developing the basic theory, a set of orthogonal backward prediction error fields for successive lattice parameter model stages is presented.