Minimal Realization of a Class of 2D Filters

It is well known that, unlike the ID case, it is not always possible to find a minimal state-space realization for a general 2D filter or system described by a transfer function except for some particular categories. The purpose of this paper is to explore the possibility of minimal Roesser model realization for a class of 2D filters or systems which does not belong to the clarified categories. As main results, a constructive realization procedure is first proposed, which can be viewed as a kind of generalization of the well-known ID realization approaches. Based on the proposed procedure, a sufficient condition for the existence of minimal realization of the considered class of 2D filters is derived, and the construction of such a minimal realization is shown. In addition, some further possible variations and applications of the obtained results are discussed and several illustrative examples are presented to show the details and effectiveness of the proposed approach