Efficient algorithms for 1-D and 2-D noncasual autoregressive system modelings

Autoregressive (AR) models have been proved to be a powerful tool in many 1-D and 2-D digital signal processing applications. Most of the work done so far, was limited to causal AR models. However, recently there has been a lot of interest to noncausal AR models. This is due to the fact that noncausal models are a more natural choice for many applications. The purpose of this paper is twofold. First, we introduce and investigate two system modeling problems, namely noncausal linear-phase AR (NCLPAR) 1-D modeling for stationary signals and noncausal zero-phase AR (NCZPAR) modeling for 2-D homogeneous random fields. Then, we introduce two efficient computational algorithms for the determination of model parameters. Finally, we illustrate the performance of the 2-D algorithms in an image restoration application.