Design of separable-denominator 2-D digital filters using the reduced-dimensional decomposition model

A separable-denominator 2-D digital filter (SD-2DDF) can be decomposed into the cascade form of a pair of 1-D digital filters (1DDFs) with different delay elements. Based on this reduced-dimensional decomposition, in this paper, we propose a new technique for designing SD-2DDFs in the spatial domain. The technique determines the coefficient matrices of 1DDFs by nonlinear optimization techniques first, and then a SD-2DDF can be easily synthesized. In addition, since the existent 1-D linear system realization techniques can be used to choose a good starting point for the optimization, extremely accurate design results can be easily achieved.