Modelling and Simulation of Images by Reciprocal Processes

In this paper we propose an approach to image modelling and simulation, by a simple class of linear constant parameter stochastic models known as stationary rciprocal processes. These processes can be seen as a special class of Gibbs-Markov random fields. Stationary reciprocal processes admit constant parameter descriptor type representations of a certain kind which can be seen as a natural non-causal extension of the linear state space models used in time series analysis. Estimation and identification of these models starting from observed data is solvable by fast and efficient numerical techniques. In particular it turns out that the statistical estimation and simulation of stationary reciprocal models leads to an extension problem for symmetric positive-definite block-circulant matrices which can be solved by Fourier methods.