Solution for the problem of the parameters identification for autoregressions with multiple roots of characteristic equations

When describing a real image using a mathematical model, the problem of model parameters identification is of importance. In this case the identification itself is easier to perform when a particular type of model is known. In other words, if there is a number of models characterized by different properties, then if there is a correspondence with the type of suitable images, then the model to be used can be determined in advance. Therefore, in this paper, we do not consider the criteria for model selection, but perform the identification of parameters for autoregressive models, including those with multiple roots of characteristic equations. This is due to the fact that the effectiveness of identification is verified by the images generated by this model. However, even using this approach where the model is known, one must first determine the order of the model. In this regard, on the basis of YuleWalker equations, an algorithm for determining the order of the model is investigated, and the optimal parameters of the model are also found. In this case the proposed algorithm can be used when processing real images.