New results on minimal realization of 2D filters

Unlike the ID case, it is not always possible to find a minimal state-space realization for a general 2D filter/system except for some particular categories. In the article, the possibility of minimal Roesser model realization for a class of 2D filters, which does not belong to the clarified categories, is explored. A constructive realization procedure is first proposed, which can be viewed as a kind of generalization of the well-known 1D realization approaches. Based on the proposed procedure, minimal realization is constructed for the 2D filters with unit coefficients. Then, a sufficient existence condition for the minimal realization of the considered class of 2D filters with arbitrary coefficients is derived, and the corresponding minimal realization is obtained. Illustrative examples are presented to show the details and effectiveness of the proposed approach.