An improved 2-D lattice filter and its entropy relations

Abstract

Abstract In this paper, an improved lattice filter structure to model two-dimensional (2-D) autoregressive (AR) fields is presented. This work is the generalization of the three-parameter lattice filter developed by Parker and Kayran. The proposed structure generates four prediction error fields (one forward and three backward prediction error fields) at the first stage. After the first stage, two additional prediction error fields are generated using two of the backward prediction error fields at the output of the first stage. This leads to six prediction error fields whose linear combination defines the successive lattice stages and the reflection coefficients. A recursive relationship between the reflection coefficients of the lattice filter and the AR coefficients is derived. In addition, the new structure and the three-parameter lattice filter are compared from information-theoretic point of view. The entropy calculations are carried out for Gaussian distributed data. It is concluded that the new structure approximates the maximum entropy more closely compared to the three-parameter structure. The increase in entropy naturally leads to a more reliable and better modelling of AR data fields.