Characterization and Estimation of Two-Dimensional ARMA (Autoregressive Moving Average) Models.
PURDUE UNIV LAFAYETTE IN SCHOOL OF ELECTRICAL ENGINEERING
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A class of finite order two dimensional autoregressive moving average ARMA is introduced having the ability to represent any process with rational spectral density. In this model, the driving noise is correlated and need not be Gaussian. Currently known classes of ARMA models of AR models are shown to be subsets of the above class. This document discusses the three definitions of markov property and precisely states the class of ARMA model having the noncausal and semicausal markov property without imposing any specific boundary conditions. Next it considers the estimation of parameters of a model to fit a given image. Two approaches are considered. The first method uses only the empirical correlations and involves the solution of linear equations. The second method is the likelihood approach. Since the exact likelihood function is difficult to compute, the author resorts to approximations suggested by the torodial models. The quality of th two estimation schemes are compared via numerical experiments. Finally, he considers the problem of synthesizing a texture obeying an ARMA model. Author
- Statistics and Probability