Accepted Manuscript

Title: An Improved Recursive and Adaptive Median Filter forHigh Density Impulse Noise

Author: Saroj K. Meher Brijraj Singhawat

PII: S1434-8411(14)00172-1DOI: http://dx.doi.org/doi:10.1016/j.aeue.2014.06.006Reference: AEUE 51234

To appear in:

Received date: 18-11-2013Revised date: 20-6-2014Accepted date: 21-6-2014

Please cite this article as: Saroj K. Meher, Brijraj Singhawat, An ImprovedRecursive and Adaptive Median Filter for High Density Impulse Noise,AEUE - International Journal of Electronics and Communications (2014),http://dx.doi.org/10.1016/j.aeue.2014.06.006

This is a PDF file of an unedited manuscript that has been accepted for publication.As a service to our customers we are providing this early version of the manuscript.The manuscript will undergo copyediting, typesetting, and review of the resulting proofbefore it is published in its final form. Please note that during the production processerrors may be discovered which could affect the content, and all legal disclaimers thatapply to the journal pertain.

Page 1 of 15

Accep

ted

Man

uscr

ipt

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

An Improved Recursive and Adaptive Median Filter

for High Density Impulse Noise

Saroj K. Meher and Brijraj Singhawat

Systems Science and Informatics Unit,Indian Statistical Institute,8th Mile, Mysore Road,

Bangalore-560059, INDIA,Ph:+918028483002-534, e-mail: (saroj.meher@isibang.ac.in), (sbrijraj@gmail.com)

Abstract

An improved recursive and adaptive median filter (RAMF) for the restoration of images

corrupted with high density impulse noise is proposed in the present paper. Adaptive

operation of the filter is justified with the variation in size of working window which is

centered at noisy pixels. Based on the presence of noise-free pixel(s), the size of working

window changes. The noisy pixels are filtered through the replacement of their values using

both noise-free pixels of the current working window and previously processed noisy pixels

of that window. These processed noisy pixels are obtained recursively. The combined

effort thus provides an improved platform for filtering high density impulse noise of images.

Experimental results with several real-time noisy images show that the proposed RAMF

outperforms other state-of-the-art filters quantitatively in terms of peak signal to noise ratio

(PSNR) and image enhancement factor (IEF). The superiority of the filter is also justified

qualitatively through visual interpretation.

Keywords:

Image restoration, impulse noise, noise filtering, adaptive median filter.

1. Introduction

The present generation of technology generates and processes huge amount of informa-

tion, particularly in the form of images. Because of several reasons, e.g., instrumental faults

during acquisition and transmission, these images are contaminated with various types of

noises. The most common type can be broadly categorized by two noise generation models,

namely, Gaussian noise and impulse noise. Gaussian noise is characterized by adding a

value to each image pixel that has a zero-mean Gaussian distribution. In turn, the noise

Preprint submitted to AEU - International Journal of Electronics and Communications June 20, 2014

*Manuscript

Page 2 of 15

Accep

ted

Man

uscr

ipt

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

affects all pixels of the image. The most common approach for reducing this noise is to

use the zero-mean distribution property, which can be realized by average of neighbor pixel

values [1]. There are two models of impulse noise generation, namely, fixed valued (also

called salt and pepper) and random valued impulsive noise. Fixed valued noise, i.e., salt

and pepper noise changes the pixel value of an image into 0 or 255, where as random valued

impulse noise changes the intensity value into a random value in the dynamic range, e.g.,

[0,5] and [250,255]. Impulse noise replaces a subset of image pixels with noise values, leaving

the remainder unchanged. The present study focuses mainly in designing filters for fixed

impulse noise values of 0 and 255, and provides a brief description about its performance for

the random impulse noise. The need to remove salt and pepper noise is imperative before

any kind of subsequent image processing tasks, such as edge detection or segmentation,

because occurrence of this noise can severely damage the information or data embedded in

the original image and makes them unusable.

One of the simplest and most popular methods to suppress salt and pepper noise is

to perform filtering operation with a conventional median filter [1, 2] that operates on a

working window, centered at the processing pixel of an image. The basic drawback of this

filter is that it performs the operation on all pixels and does not effectively reduces the noise

with the protection of edges and detail information of image. Several modified versions of

the median filter, e.g., [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], have been proposed

using a noisy pixel detector, in order to skip the processing of noise-free pixels and preserve

the necessary image details. The effectiveness of these approaches depends highly on the

performance of the noisy pixel detector [17]. The present study does not put more efforts in

the detection of noisy pixels and aims at designing improved filters which faithfully works

to filter the high density noise of an image even in the presence of a less efficient detector.

In a similar effort, recently, Esakkirajan et. al [13] have proposed a modified decision-

based unsymmetrical trimmed median filtering (MDBUTMF) method to filter both gray-

scale and color images. The filter could preserve certain extent of image details at low

density impulse noise, i.e., below 50%. However, at high density noise, i.e., above 50%, the

performance of MDBUTMF deteriorates. The possible reason is that at high density noise,

most/all pixels of the working window are noisy and the filter substitutes the processing

noisy pixel with the mean of adjacent noisy pixels. In turn, the substituted processing

pixels are is approximated by noisy pixels and lead to noisy values.

2

Page 3 of 15

Accep

ted

Man

uscr

ipt

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

In another attempt, Srinivasan and Ebenezer [8] have described a filtering method based

on some decisions (DBF), which works fairly well for images contaminated with high density

impulse noise. They demonstrated the usefulness of DBF in filtering noisy images corrupted

with high density noise. The method provides improved results compared to conventional

median filter and other modified versions at high density noise. Generaly, at high density

of noise, all the neighbor pixels of the center noisy pixel of working window are noisy

and to combat this DBF substitutes the noisy pixels by taking the support of previously

processed noisy pixels that are obtained recursively. However, the method did not provide

any procedure for using the adjacent neighbors of previously processed pixels of that image,

which leads to an average performance of filter in the whole process. In a similar approach,

Tan et al. [12] proposed a neighborhood mean filtering (NMF) method for high density noise,

where the processing pixel is replaced by the mean of these neighbors that are obtained

recursively. With this approach, NMF could overcome the pitfall of DBF method [8] and

provides improved performance at high density of noise. The drawback in this approach is

that at low density noise, the filter replaces the noisy pixels with the mean of the noise-free

pixel(s) present in the working window. However, the mean operation performed by NMF

for both low and high density noises, smoothes the fine details and edges of the image.

In the present study, we have proposed an improved recursive and adaptive median

filter (RAMF) for high density impulse noise that overcomes the drawbacks of these above

mentioned methods (MDBUTMF, DBF and NMF). The basic motivation in the develop-

ment of the RAMF method is to integrate the merits of these methods synergistically and

design a filter that performs superior to the state-of-the-art methods both at low and high

densities noises. The RAMF restores the fine details and image integrity in the filtering

process potentially and performs significantly better than others. The superiority of the

proposed method to adaptive median filter (AMF) [18], decision-based filter (DBF) [8],

neighborhood mean filter (NMF) [12], and modified decision-based unsymmetrical trimmed

median filtering (MDBUTMF) [13], is justified both qualitatively and quantitatively with

nine benchmark images (corrupted with different levels of impulse noises) using peak signal-

to-noise ratio (PSNR) and image enhancement factor (IEF) [8, 13].

Remaining part of the paper is organized as follows. Motivation in the development of

the proposed filtering method is described in Section 2. Section 3 describes the step-by-step

procedure and advantages of the method. Simulation results with discussions are illustrated

3

Page 4 of 15

Accep

ted

Man

uscr

ipt

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

in Section 4. Finally, Section 5 provides the conclusions and future scopes of the present

work.

2. Motivation

The motivation in the development of an improved recursive and adaptive median fil-

ter is based on the merits of three existing methods (DBF, NMF and MDBUTMF), as

described in the previous section. Decision based method, i.e., DBF at high density of

noise substitutes the noisy pixels with adjacent neighbor pixel values that is obtained in

the previous processing step. The disadvantage in this process is that it does not have the

selection and usage procedures for these pixels and thus provides an average performance.

This motivated us to take a consensus decision with proper assessment of these neighbors.

In a similar attempt, NMF method proposed to use the mean of neighbors in replacing the

noisy pixel, when all the pixels of the working window are noisy. The method also uses mean

operation at low density of noise, and thus smoothes the image which leads to the loss of

lines and fine detail (edge) information. MDBUTMF performs the mean operation on the

neighboring pixels of center pixel if all neighbor pixels are noisy. This step of MDBUTMF

tries to approximate the pixel value with the help of noisy pixels that finally produces

nearly noisy value. This encouraged us to use the median operation in the replacement of

the noisy pixels in stead of mean.

These three methods further motivated us to inspect the next size of working window,

i.e., (5 x 5), if all the pixels are noisy in (3 x 3) window. If we find any noise-free pixel(s)

in (5 x 5) window then the processing noisy pixel will be replaced with the median of those

pixels. If all the pixels are noisy, then the processing noisy pixel will be replaced by the

median of already processed four adjacent neighbor pixels in the (3 x 3) window. This step

thus works with an adaptive manner in selecting the working window size. The proposed

filter also rectifies the noisy pixels that nearly approximate the original value of the noisy

pixel. In the following section, we have provided the complete algorithm of the proposed

RAMF method for the convenience of understanding the process.

3. Proposed filtering method

In the present study, we have used the fixed valued impulse noise model called salt

and pepper noise, which consists of two extreme gray-level values of the image with equal

4

Page 5 of 15

Accep

ted

Man

uscr

ipt

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

probability. For an 8-bit image, these fixed values are 0 and 255. With this noise, a certain

amount of pixels in the image are either black or white corresponding to value 0 or 255,

respectively. Given the probability z (with 0 6 z 6 1) that a pixel is corrupted, we can

introduce salt and pepper noise in an image by setting a fraction of z = 2 randomly selected

pixels of the image to black with a value 0, and another fraction of z = 2 randomly selected

pixels to white with a value 255. In the proposed impulse noise filtering model (RAMF), the

pixels of the image are separated into noisy and noise-free categories using a simple method

that is computationally efficient [19]. This method works based on the histogram analysis

of image, where the categories of pixels are determined by two noisy peaks of histogram.

These two peaks are the first peaks encountered by passing through the histogram, i.e.,

from left-side end and right-side end toward the center of histogram. Hence, pixel values

between these two peaks are classified as noise-free and others as noisy pixels. The proposed

method is operated on the noisy pixels only leaving the noise-free pixels unchanged. We

have used this simple noisy pixel classification method to avoid the possibility of classifying

some noise-free pixels as noisy and help the next step of filtering operation more efficient.

The complete steps of the algorithm are as follows.

1. Take a pixel x[r, c] from the image and consider a (3 x 3) working window centers at

x[r, c],

2. Classify x[r, c] as noisy or noise-free. If it is noise-free, then its value is left unchanged.

Otherwise, it is processed for filtering in the next step,

3. If x[r, c] is noisy, then two cases arise,

(a) Case 1: If (3 x 3) window contains one or more noise-free pixels (as classified

initially), then replace x[r, c] with the median of these pixel(s),

(b) Case 2: If all pixels in (3 x 3) window are noisy, then increase the size of working

window from (3 x 3) to (5 x 5), then two sub-cases arise,

i. Sub-case 1: If (5 x 5) window contains one or more noise-free pixels, then

replace x[r, c] with the median of these pixel(s),

ii. Sub-case 2: If all pixels of this (5 x 5) window are noisy, then replace x[r, c]

by the median of already processed four adjacent neighboring pixels in the

(3 x 3) window,

4. Repeat steps 1 to 3 until all the pixels in the entire image are processed.

5

Page 6 of 15

Accep

ted

Man

uscr

ipt

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

RIVER HOUSE OWL

LAKE SCENERY BABOON

BRIDGE BUTTERFLY BOAT

Figure 1: Nine test images (original).

6

Page 7 of 15

Accep

ted

Man

uscr

ipt

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

4. Results and discussions

The present study justifies the superiority of the proposed recursive and adaptive median

filtering (RAMF) method to several state-of-the-art methods and demonstrates its image

restoration capability on different benchmark images contaminated with varying level of

impulse noise densities. Nine benchmark test images (Fig. 1) of sizes (512 x 512) are used

for the simulation purpose. These images are, namely, RIVER, HOUSE, OWL, LAKE,

SCENERY, BABOON, BRIDGE, BUTTERFLY and BOAT. We have provided the detail

results and descriptions of RIVER image only in the result section because similar trend of

performance was observed for all the nine images. However, for 90% noise density, perfor-

mance comparative results of various methods are illustrated for all the images to justify

the superiority of the proposed method over others at high density of noise. The image

restoration operation is performed at different noise densities varied from 10% to 90% with

the increment of 10%. The performance of the proposed RAMF method is compared with

five state-of-the-art filtering methods, such as adaptive median filter (AMF) [18], decision-

based filter (DBF) [8], neighborhood mean filter (NMF) [12], and modified decision-based

unsymmetrical trimmed median filtering (MDBUTMF) [13]. The comparative analysis is

made in terms of objective testing (quantitative evaluation) using peak signal to noise ratio

(PSNR) and image enhancement factor IEF [8, 13], and subjective testing (visual quality).

The indexes PSNR and IEF can be defined as:

PSNR = 10 log10

2552

1

RC

R∑

r=1

C∑

c=1

(x[r, c]− x[r, c])2

, and (1)

IEF =

R∑

r=1

C∑

c=1

(y[r, c]− x[r, c])2

R∑

r=1

C∑

c=1

(x[r, c]− x[r, c])2

. (2)

Here x[r, c], y[r, c] and x[r, c] denote the pixels of original, noisy and restored images at

position [r, c], respectively for an 8-bit image.

All the experimental analyses performed in the present study are providing different

results although the experimental conditions are same. This is because the experiments are

dealing with randowmly generated noise. Hence, each experiment is repeated for ten times

with the same conditions and the average of these values is presented in the result section.

7

Page 8 of 15

Accep

ted

Man

uscr

ipt

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Table 1: Comparative results in PSNR of various filtering methods for RIVER image at different noise

densities

Noise PSNR in dB

density AMF DBF NMF MDBUTMF RAMF

(in %) (proposed)

10 27.11 35.71 23.54 35.76 36.12

20 25.32 31.42 22.61 31.63 32.24

30 23.14 28.17 21.68 28.39 30.19

40 21.11 25.54 20.69 25.63 27.12

50 20.25 23.19 20.79 24.13 25.42

60 17.15 19.56 19.87 20.04 23.04

70 12.15 16.12 19.43 12.54 20.61

80 4.67 13.31 17.87 4.17 18.58

90 3.10 11.11 14.43 3.7 15.76

Table 2: Comparative results in IEF of various filtering methods for RIVER image at different noise densities

Noise IEF

density AMF DBF NMF MDBUTMF RAMF

(in %) (proposed)

10 146.54 174.16 18.13 176.49 179.97

20 135.26 155.26 36.90 159.02 160.91

30 120.02 144.11 54.30 145.22 148.30

40 98.81 126.23 68.94 128.09 132.29

50 77.17 91.03 80.57 102.92 118.59

60 67.18 80.26 84.11 67.32 104.55

70 32.05 61.70 79.24 33.88 90.77

80 20.93 40.05 58.48 15.23 74.00

90 10.11 25.54 32.18 6.67 51.36

8

Page 9 of 15

Accep

ted

Man

uscr

ipt

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Table 3: Comparative results of various filtering methods for nine different images at 90% noise density

AMF DBF NMF MDBUTMF RAMF

(proposed)

Image PSNR IEF PSNR IEF PSNR IEF PSNR IEF PSNR IEF

RIVER 3.10 10.11 11.11 25.54 14.43 32.18 3.7 6.67 15.76 51.36

BABOON 5.01 8.85 7.12 11.27 10.04 13.48 5.72 9.08 14.84 19.82

SCENERY 5.92 8.34 4.01 9.24 13.64 54.78 3.49 9.31 17.48 83.27

BOAT 5.01 9.52 2.97 10.25 10.55 46.79 4.28 9.02 17.28 60.29

BRIDGE 2.76 10.30 3.01 10.47 10.92 27.19 3.22 7.87 15.09 40.79

BUTTERFLY 6.12 11.11 6.75 11.23 12.97 55.50 4.92 10.52 19.72 76.65

HOUSE 5.53 5.18 5.74 5.76 8.89 20.70 2.12 4.86 10.44 31.64

LAKE 8.19 7.91 8.33 7.93 13.27 27.26 2.08 7.16 16.22 38.95

OWL 8.84 8.23 9.01 8.42 15.54 48.68 1.4 7.24 17.01 60.16

For all the five filtering methods, the comparative simulated results in terms of PSNR

values with RIVER image corrupted at different noise densities, are illustrated in Table 1.

It is observed from the Table 1 that at low noise densities (i.e., about below 50%), both

DBF and MDBUTMF provide fair and similar level of performances, which get deteriorated

at high noise densities. The reason behind this is that at low density noise both DBF and

MDBUTMF replace the noisy pixels with the help of noise-free pixels of the working window,

but at high noise density, i.e., when all the pixels of the working window are noisy, althoigh

DBF takes support from the previously processed pixels, it does not follow any procedure to

use them, and MDBUTMF makes use of noisy pixels only. Comparatively, DBF performs

well than MDBUTMF at high density of noise. Interestingly, NMF performs poorer at low

noise densities and comparatively better than MDBUTMF and DBF at high noise densities.

The reason behind this fact is that at high noise densities, NMF makes use of previously

processed pixels of image by taking their mean, when the pixels of the working windows

are noisy. In another comparative analysis, the AMF performed consistently from low to

high noise densities. However, the proposed RAMF method outperformed these methods

at all noise densities that justified the reason for the synergistic integration of the merits

of different methods. The superiority of the proposed RAMF method to others is also

validated with the IEF values in Table 2. All the critically assessed improved performance

obtained with the PSNR is justified and supported the superiority claim of the proposed

improved recursive and adaptive median filtering model with IEF measure. We have also

9

Page 10 of 15

Accep

ted

Man

uscr

ipt

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

provided the comparative results with PSNR and IEF values for all the images at high

density noise, i.e., 90% in Table 3. The promising claim with RAMF method is also true

for all the images at high density noise.

(a) (b) (c)

(d) (e) (f)

Figure 2: RIVER image: (a) Noisy (90%), restored images using (b) AMF [18], (c) DBF [8], (d) NMF [12],

(e) MDBUTMF [13], and (f) RAMF (proposed)

So far we have discussed the advantages of RAMF method over others quantitatively.

We have also provided the qualitative results with a visual observation of comparison for

RIVER image at 90% noise density, which reflects the similar observation as obtained with

PSNR and IEF values. The noisy and corresponding restored images are shown in Fig. 2.

The proposed RAMF method improved the filtering efficiency significantly and performed

superior to others in preserving the necessary image details even for highly corrupted images,

as shown in Fig. 2. A zoomed version of a small region of the restored images using different

filters is shown in Fig. 3 to have an improved visualization. In addition, with four noise

densities (i.e., 10%, 30% , 60% and 90%), the qualitative results are shown in Fig. 4 using

10

Page 11 of 15

Accep

ted

Man

uscr

ipt

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

(a) (b)

(c) (d) (e)

Figure 3: Zoomed regions of RIVER image as restored in Fig. 2 using: (a) AMF, (b) DBF, (c) NMF, (d)

MDBUTMF, and (e) RAMF (proposed)

11

Page 12 of 15

Accep

ted

Man

uscr

ipt

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

(A) (E) (I)

(B) (F) (J)

(C) (G) (K)

(D) (H) (L)

Figure 4: RIVER image with noise (A) 10%, (B) 30% , (C) 60% and (D) 90%, and their corresponding

restored versions using (E-H) AMF and (I-L) RAMF methods (proposed).12

Page 13 of 15

Accep

ted

Man

uscr

ipt

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

two methods of filters, such as AMF and RAMF. Similar trend is also observed in this case.

The regions obtained using the proposed restoration method are more crisp, distinct, and

their edges and fine details are more prominent compared to the regions obtained using other

method. These observations further justify the significance of the PSNR and IEF indexes

in reflecting the performance of the models automatically without visual intervention.

It is worth to mention here that the proposed RAMF filtering method is restoring the im-

ages in an improved way compared to others for random impulse noise values also. However,

its performance deteriorates above the dynamic range of [0,5] and [250,255]. Intuitively, the

efficacy of the method is justified by using the simple and effective searching of noisy peaks

from the histogram of the image, to separate the noisy pixels from noise-free pixels (Section

3). Our future study in this regard is to achieve further improvement and applicability

of the approach to random impulse noise of large dynamic range. Moreover, this would

essentially require a robust detection method for noisy pixels.

5. Conclusions

The present paper proposed an improved recursive and adaptive median filtering (RAMF)

method for fixed-value impulse noise at high density. The performance of RAMF method

was compared with four other methods, such as AMF, DBF, NMF and MDBUTMF in

terms of two measurement indexes, namely PSNR and IEF. It was observed through the

experimental results that the RAMF method could restore the images with better accuracy

than others at high density of noise. Both qualitatively and quantitatively the RAMF was

found to the superior than others in preserving necessary fine lines, edges and image details.

References

[1] R. C. Gonzalez, R. E. Woods, Digital Image Processing, 3rd Edition, Prentice Hall,

New Jersey, USA, 2008.

[2] W. K. Pratt, Median filtering, Tech. rep., Image Proc. Inst. Univ. Southern California,

Los Angeles (1975).

[3] T. Nodes, N. Gallagher, Median filters: Some modifications and their properties, IEEE

Trans. Acoust., Speech, Signal Process. ASSP-30 (1982) 739–746.

13

Page 14 of 15

Accep

ted

Man

uscr

ipt

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

[4] S.-J. Ko, S.-J. Lee, Center weighted median filters and their applications to image

enhancement, IEEE Trans. Circuits Syst. 15 (1991) 984–993.

[5] J.-Y. Chang, J.-L. Chen, Classifier-augmented median filters for image restoration,

IEEE Trans. Inst. and Meas. 53 (2004) 351–356.

[6] M. E. Yuksel, A. Bastrk, A simple generalized neuro-fuzzy operator for efficient removal

of impulse noise from highly corrupted digital images, AEU-International Journal of

Electronics and Communications 59 (2005) 1–7.

[7] M. E. Yuksel, A median/ANFIS filter for efficient restoration of digital images cor-

rupted by impulse noise, AEU-International Journal of Electronics and Communica-

tions 60 (2006) 628–637.

[8] K. S. Srinivasan, D. Ebenezer, A new fast and efficient decision-based algorithm for

removal of high-density impulse noises, IEEE Signal Process. Lett. 14 (2007) 189–192.

[9] W. Luo, An efficient algorithm for the removal of impulse noise from corrupted images,

AEU-International Journal of Electronics and Communications 61 (2007) 551–555.

[10] H. Ibrahim, N. S. P. Kong, T. F. Ng, Simple adaptive median filter for the removal

of impulse noise from highly corrupted images, IEEE Trans. Consumer Electronics 54

(2008) 1920–1927.

[11] C.-C. Kang, W.-J. Wang, Modified switching median filter with one more noise detector

for impulse noise removal, AEU-International Journal of Electronics and Communica-

tions 63 (2009) 998–1004.

[12] X. Tan, Q. Zhang, D. Zha, A new salt and pepper noise removal filtering algorithm,

in: Proceedings of 2010 Conference on Dependable Computing (CDC2010), 2010, pp.

129–131.

[13] S. Esakkirajan, T. Veerakumar, A. N. Subramanyam, C. H. PremChand, Removal

of high density salt and pepper noise through modified decision based unsymmetric

trimmed median filter, IEEE Signal Process. Lett. 18 (2011) 287–290.

[14] I. Turkmen, Efficient impulse noise detection method with anfis for accurate image

14

Page 15 of 15

Accep

ted

Man

uscr

ipt

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

restoration, AEU-International Journal of Electronics and Communications 65 (2011)

132–139.

[15] B. Xiong, Z. Yin, A universal denoising framework with a new impulse detector and

nonlocal means, IEEE Trans. Image Process. 21 (2012) 1663–1675.

[16] S. K. Meher, Recursive and noise-exclusive fuzzy switching median filter for impulse

noise reduction, Engineering Applications of Artificial Intelligence 30 (2014) 145–154.

[17] S. K. Meher, P. Patel, Fuzzy impulse noise detector for efficient image restoration, in:

IEEE Conf. on Recent Advances in Intelligent Computational Systems (RAICS-2011),

2011, pp. 701–705.

[18] H. Hwang, R. A. Haddad, Adaptive median filters: New algorithms and results, IEEE

Trans. Image Process. 4 (1995) 499–502.

[19] K. K. V. Toh, H. Ibrahim, M. N. Mahyuddin, Salt-and-pepper noise detection and

reduction using fuzzy switching median filter, IEEE Trans. Consumer Electronics 54

(2008) 1956–1961.

15