In this paper, we propose a two-dimensional (2-D) least-squares lattice (LSL) algorithm for the general case of the autoregressive (AR) model with an asymmetric half-plane (AHP) coefficient support. The resulting LSL algorithm gives both order and space recursions for the 2-D deterministic normal equations. The size and shape of the coefficient support region of the proposed lattice filter can be chosen arbitrarily. Furthermore, the ordering of the support signal can be assigned arbitrarily. Finally, computer simulation for modeling a texture image is demonstrated to confirm the proposed model gives rapid convergence.

In the adaptive lattice estimation process, it is well known that the convergence speed of the successive stage is affected by the estimation errors of reflection coefficients in its preceding stages. In this paper, we propose block estimation methods of two-dimensional (2-D) adaptive lattice filter. The convergence speed of the proposed algorithm is significantly enhanced by improving the adaptive performance of preceding stages. Furthermore, this process can be simply realized. The modeling of 2-D AR field and texture image are demonstrated through computer simulations.

The present paper examines a two-dimensional (2-D) joint-process lattice estimator and its implementation for image restoration. The gradient adaptive lattice (GAL) algorithm is used to update the filter coefficients. The proposed adaptive lattice estimator can represent a wider class of 2-D FIR systems than the conventional 2-D lattice models. Furthermore, its structure possesses orthogonality between the backward prediction errors. These results in superior convergence and tracking properties versus the transversal and other 2-D adaptive lattice estimators. The validity of the proposed model for image restoration is evaluated through computer simulations. In the examples, the implementation of the proposed lattice estimator as 2-D adaptive noise cancellator (ANC) and 2-D adaptive line enhancer (ALE) is considered.

We present an extended quarter-plane lattice model for generating two-dimensional (2-D) autoregressive fields. This work is a generalization of the extended lattice filter of diagonal form (ELDF) developed by Ertuzun et al. The proposed model represents a wider class of 2-D AR fields than conventional lattice models. Several examples are presented to demonstrate the applicability of the proposed model. Furthermore, the proposed structure is compared with other conventional lattice filters based on the computation of their entropy values.

The present paper investigates a two-dimensional (2-D) adaptive lattice filter used for modeling 2-D AR fields. The 2-D least mean square (LMS) lattice algorithm is used to update the filter coefficients. The proposed adaptive lattice filter can represent a wider class of 2-D AR fields than previous ones. Furthremore, its structure is also shown to possess orthogonality in the backward prediction error fields. These result in superior convergence and tracking properties to the adaptive transversal filter and other adaptive 2-D lattice models. Then, the convergence property of the proposed adaptive LMS lattice algorithm is discussed. The effectiveness of the proposed model is evaluated for parameter identification through computer simulation.