Causal and semicausal AR image model identification using the EM algorithm

The method presented by T. Katayama and T. Hirai (1990), who considered the problem of semicausal autoregressive (AR) parameter identification for images degraded by observation noise, is extended. In particular, an approach to identifying both the causal and semicausal AR parameters without a priori knowledge of the observation noise power is proposed. The image is decomposed into 1-D independent complex scalar subsystems resulting from the vector state-space model, using the unitary discrete Fourier transform (DFT). Then the expectation-maximization algorithm is applied to each subsystem to identify the AR parameters of the transformed image. The AR parameters of the original image are then identified using the least-square method. The restored image is obtained as a byproduct of the EM algorithm.