Median-Rational Hybrid Filters

In this paper we introduce a new class of nonlinear filters called Median-Rational Hybrid Filters (MRHF) based on Rational Functions (RF). The filter output is the result of a rational operation taking into account three sub-functions, such as two FIR or median subfilters and one center weighted median filter (CWMF). The proposed MRHF filters have the inherent property that on smooth areas they provide good noise attenuation whereas on changing areas the noise attenuation is traded for good response to the change. The performance of the proposed filter is compared against widely known nonlinear filters such as: Morphological Signal Adaptive Median Filters, Stack Filters, RankOrder Morphological Filters and simple Rational Filters. shaped mask. [6] based on the work of Walsh [12] for signal detection and estimation and were later applied by Ramponi in [7] ,[8] for image filtering and enhancement. It was later extended to deal with multidimentional data, in [4], for color image interpolation. Specifically, in the image restoration problem, the rational filter developed in [7] , performs well for relatively high S N R Gaussian contaminated environments. In order to derive a rational filter to deal with various kinds of noise such as Gaussian noise, impulsive noise and mixed Gaussian-impulsive noise, we propose a new class of nonlinear rational type hybrid filters for signal and image processing called Median-Rational Hybrid (MRH) Filters. The MRH Filter is based on three sub-operators in which the central sub-operator is a center weighted median CWM filter acting on a plusAn outline of the paper is as follows. Section 2 describes the Median Rational Hybrid Filters in one and two dimensional cases and points some its important properties. Section 3 includes experimental results; while, section 4 concludes the paper. It is shown that a significant subjective improvement in the restored image quality as well as a consistent reduction in the objectively measured mean absolute error and mean square error is obtained.