Programmable Hardware Implementation for the Median-Rational Hybrid Filters

The Median-Rational Hybrid Filter (MRHF) has been recently introduced [1][2] as a new class of nonlinear filters and successfully applied to image filtering problems. The main characteristics of the MRHF are the good noise attenuation property in smooth areas and the preservation of edges end details. In fact, in changing areas the noise attenuation is traded for a good response to the change. Moreover, the median filters effectively remove the impulsive noise while the rational filter performs well in relatively high SNR Gaussian contaminated environments. Another relevant characteristic is that MRHF’s usually act on small windows and thus require a reduced number of operations, resulting in simple and fast filtering structures. In this paper we present a programmable hardware implementation for the MRHF’s. Exploiting the features of the dynamic logic families i t is possible to achieve high speed and compactness, while keeping the power dissipation very low. One component of the MRHF’s is a rational operator, i.e. a ratio of two polynomials. There are several advantages in the use of this operator. In fact, a rational function can approximate any continuous function arbitrarily well as a polynomial function does, but achieving a desired level of accuracy with a lower complexity. The second component of the MRHF’s is a set of median filters which are effective in removing impulsive noises. l’herefore, the MRHF uses a two-step a,pproach to remove both impulsive and Gaussian noises from an image. Its structure contains two median filters (MF) and one center weighted median filter (CWMF); the ouputs of these filters are the input to a rational filter whose input-output relationship is a simple rational function. Therefore, while the median filters effectively remove the impulsive noise, the rational filter [4] offers good prcformances in relatively high S N R Gaussian contaminated environments. When both impulsive and Gaussian noises spoil the images the MRHF outperforms other nonlinear filters because it exploits at the same time the fealures of both median and rational filters.