Design Constraints For Polynomial And Rational Filters

Polynomial and rational filters for image enhancement, edge preserving noise smoothing, and interpolation of encoded images are usually designed as a weighted combination of nonlinear filters having lowpass or highpass behaviour. The choice of the filter components and of the coefficients is performed heuristically, though. In this paper general design constraints for polynomial and rational filters are presented that are necessary to achieve isotropy, the preservation of the expectation value, and the detection of edges. For the application of edge preserving noise smoothing a method is derived to find an optimal polynomial or rational filter that meets these constraints. 1. INTRODUCTION Polynomial and rational filters have shown to be a successful tool for applications in image enhancement, edge preserving noise smoothing, and interpolation of encoded images [1, 4, 6, 7, 8, 9]. Their design is usually based on a weighted combination of nonlinear filters having lowpass or highpass beh..