Subspace System Identification of Separable-in-Denominator 2-D Stochastic Systems

The fitting of a causal dynamic model to an image is a fundamental problem in image processing, pattern recognition, and computer vision. There are numerous other applications that require a causal dynamic model, such as in scene analysis, machined parts inspection, and biometric analysis, to name only a few. There are many types of causal dynamic models that have been proposed in the literature, among which the autoregressive moving average (ARMA) and state-space models are the most widely known. In this paper we introduce a 2-D stochastic state-space system identification algorithm for obtaining stochastic 2-D, causal, recursive, and separable-in-denominator (CRSD) models in the Roesser state-space form. The algorithm is tested with a real image and the reconstructed image is shown to be almost indistinguishable to the true image.