Sequentially combined mean-median filter for high density salt and pepper noise removal

Salt and pepper noise removal is extremely challenging task when the noise density is very high in the corrupted image. Usually the existing filters are not capable of removing this noise above 70% density. This paper proposes a Sequentially Combined Mean-Median Filter (SCMMF) based on combination of arithmetic mean and median technique. A binary flag image is generated with the help of identified noisy pixels which are first replaced by a value calculated by plus (+) operation with nearest pixels intensities. The remaining noisy pixels are then replaced by neighbourhood mean operations. Finally the image quality is enhanced by the median of the corresponding window. Border operation is also incorporated to preserve the image size. Experimental results show that SCMMF is outstanding from visual qualitative judgments for a number of standard images. Moreover, this combined filter outperform over the existing with respect to MSE, PSNR, and SSIM comparison even at 92% noise density level.

I. Introduction

SALT and pepper noise, often visible on the images, is a form of impulse noise displayed as random white and black dots. Here the noisy pixels [1] take either maximum or minimum gray levels i.e. 255 or 0, respectively. The maximum value contributes white dots and minimum value contributes black dots on the image. So this noise can be called bipolar impulse noise. In many cases the ratio of black and white dots is 1:1. This type of noise is caused by faulty image acquisition and transmission systems. To restore the noisy image many approaches [2]–[5], [7]–[21] have been proposed, e.g. Simple Median Filter (SMF) [3], Generalized Mean Filter [4], Adaptive Median Filter (AMF) [5], Decision Based Algorithm (DBA) [8], Noise Adaptive Fuzzy Switching Median Filter (NAFSMF) [11], Modified Decision Based Un-Symmetric Trimmed Median Filter (MDBUTMF) [12], Fast and Efficient Median Filter (FEMF) [13], Jourabloo Filter (JF) [14], Adaptive Window Multi-stage Median Filter (AWMMF) [15], Adaptive Weighted Mean Filter (AWMF) [18], and so on. Linear spatial filters were the first attempt towards image smoothing. In the linear spatial mean filter, noisy pixel replacement is made by the mean of the neighbourhood pixels of the corresponding window. The first and most popular simplest non-linear filter is Standard Median Filter (SMF), introduced by Tukey [2] where pixel replacement is carried out by the median of the corresponding pixel window. To overcome some limitation of the SMF, an Adaptive Median Filter (AMF) was introduced but increasing of window size leads to blurring effect. Next, repeated replacement of neighbourhood pixels was introduced by Decision Based Algorithm (DBA) which causes streaking effect. To challenge the limitations of DBA, Modified Decision Based Un-Symmetric Trimmed Median Filter (MDBUTMF) was proposed. These filters perform efficiently at low and moderate noise densities. Moreover, in recent time many filters have been noticed in the literature. For example, FEMF somehow perform better by using prior information to get natural pixels for restoration. The NAFSMF uses histogram analysis and fuzzy technique to detect and remove noises likewise. On the other hand, the concept of variation of window [7] has been taken from AMF in AWMF and the corrupted pixels are replaced by the weighted mean.