Parameter Identification of Image Models by the Recursive Maximum Likelihood Method

Abstract

This paper considers the problem of identifying the blur parameters of the observed image. It is assumed that the original image is a sample from the homogeneous random field described by a two-dimensional (2-D) semicausal model, and that the point spread function (PSF) characterizing the image blur is symmetric. It is also assumed that the observation noise is negligibly small. By applying the discrete sine transform, we derive a set of nearly uncorrelated ARMA models, which are of non-minimum phase, for the blurred image. Although all-pass components of the MA part of the models can not be estimated, we show that the parameters of the non-minimum phase MA part can be restored by exploiting the fact that the PSF is symmetric. We develop a new algorithm for identifying the blur parameters of the image model from the MA parameters estimated by the recursive maximum likelihood (RML) method. Simulation studies are also included to show the feasibility of the algorithm.