<title>Decision-based median filter using local signal statistics</title>

Abstract

ABSTRACT Noise removal is important in many applications. When the noise has impulsive characteristics, linear techniquesdo not perform well, and median filter or its derivatives are often used. Although median-based filters preserve edgesreasonably well, they tend to remove some of the finer details in the image. Switching schemes — where the filter isswitched between two or more filters — have been proposed, but they usually lack a decision rule efficient enough toyield good results on different regions of the image. In this paper we present a strategy to overcome this problem. Adecision rule based on the second order local statistics of the signal (within a window) is used to switch between theidentity filter and a median filter. The results on a test image show an improvement of around 4dB over the medianfilter alone, and 2dB over other techniques.Keywords: Median filter; Image enhancement; Noise removal; Impulsive noise. 1. INTRODUCTION Noise reduction is often necessary as a pre-processing step in situations where a signal is contaminated by noise.In cases where the noise can be adequately modeled as additive Gaussian noise, linear filters are normally efficiciitfor noise-reduction. However, in many cases the noise is impulsive, and in this case linear techniques do not usuallyperform well. The median filter and its derivatives are often the filter of choice for these applications.The median filter is a non-linear filter, and it has the useful property of removing (reducing) impulsive noisewithout (severely) smoothing the edges of the signal. The main drawback of the median filter is that it also modifiesthe points not contaminated by noise, therefore removing the finer details in the signal.In the past 20 years, median filters have been generalized and modified in many ways. A good overview of pastwork on generalizations of median filters can be find in the paper by Gabbouj et al.1 Examples include rank orderfilters, weighted median filters, stack filters, and linear combinations of nonlinear filters. A theory for optimal stackfilters has been developed.2 More recently, filters where the rank selected is based on the pixel rank have been alsoproposed .