Representation of Non-Gaussian, Finite-States, Reciprocal Processes: the 1-D Problem with Cyclic Boundary Conditions

The aim of this paper is to propose a nonlinear approach in modeling and estimation for non-Gaussian discrete-index reciprocal processes. The sub-class of the finite-states processes is taken under consideration. Such a class of processes seems to be a suitable setup in many applications, and in particular it appears well suited for image-processing. For this class of processes a stochastic realization is shown to exist in the form of a fixed-degree polynomial model. In this perpective the present paper extends to a non-Gaussian case some, well known in the literature, representation results about Gaussian reciprocal processes.