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

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 (1984). 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.