Optimum Asymmetric Half-Plane Autoregressive Lattice Parameter Modeling of 2-D Fields

In this paper, we present a new optimum asymmetric half-plane (ASHP) autoregressive lattice parameter modeling of two-dimensional (2-D) random fields. This structure introduces 4N points into the prediction support region when the order of the model increases from (N - 1) to N. Starting with a given data field, a set of four auxiliary prediction errors are generated in order to obtain the growing number of 2-D ASHP reflection coefficients at successive stages. The theory has been applied to the high-resolution radar imaging problem and has also been proven using the concepts of vector space, orthogonal projection, and subspace decomposition. It is shown that the proposed ASHP structure generates the orthogonal realization subspaces for different recurse directions. In addition to developing the basic theory, the presentation includes a comparison between the proposed theory and other alternative structures, both in terms of conceptual background and complexity. While the recently developed reduced-complexity ASHP lattice modeling structure requires O(4N³) lattice sections with N equal to the order of the error filter, the proposed configuration requires only O(2N²) lattice sections.