Median Filter for High-Density Salt-And-pepper Noise Removal in Images

8/10/2019 Median Filter for High-Density Salt-And-pepper Noise Removal in Images

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New decision-based trimmed medianfilter for high-density salt-and-pepper

noise removal in images

Vaithiyam Rengarajan VijaykumarGuru Santhanamari

wnloaded From: http://electronicimaging.spiedigitallibrary.org/ on 12/03/2014 Terms of Use: http://spiedl.org/terms


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New decision-based trimmed median filter forhigh-density salt-and-pepper noise removal in images

Vaithiyam Rengarajan Vijaykumara,* and Guru SanthanamaribaAnna University, Department of ECE, Coimbatore 641047, IndiabTamilnadu College of Engineering, Department of ECE, Coimbatore 641659, India

Abstract.A new switching-based trimmed median filter to remove high-density salt-and-pepper noise in digitalimages is proposed. Initially, a 3 3sliding window is applied on each pixel in the noisy image. The minimum-and maximum-intensity values are trimmed, and the noisy pixels are detected based on the predefined thresholdvalue. In the filtering stage, the noisy pixels are replaced by median value of uncorrupted pixels in the trimmedarray. At very high noise density, if all the pixels in the sliding window are corrupted, then the proposed algorithmreplaces noisy pixels by the midpoint of recently processed pixels. The experimental results for various testimages show that the performance of the proposed algorithm is superior to the existing algorithms, namelySMF, WMF, CWMF, AMF, DBA, and MDBUTMF in terms of visual quality and edge preservation, even atnoise levels as high as 95%. 2014 SPIE and IS&T [DOI:10.1117/1.JEI.23.3.033011]

Keywords: edge preservation; impulse noise; nonlinear filter; trimmed median filter.

Paper 13352 received Jul. 3, 2013; revised manuscriptreceivedMar. 16,2014;acceptedfor publication May2, 2014; publishedonlineJun. 9, 2014.

1 Introduction

Images are frequently corrupted by impulse noise due to mal-functioning of camera sensors, faulty memory locations inhardware, and transmission of images in noisy channels,which can seriously affect quality of the images.1 Salt-and-pepper noise is also called fixed-valued impulse noise, whichcan take two extreme-intensity values normally being theminimum (0) and the maximum (255). In an image, edgescontain essential information and the objective of any filter-ing technique is to remove the impulses, so that the edge

details should be preserved. In general, linear filtering tech-niques for image restoration tend to blur the edges. The sim-plest nonlinear filter to remove the salt-and-pepper noise isthe standard median filter (SMF).2 Median filters are widelyused due to their effective noise suppression capability andsimplicity in implementation. But at higher noise levels, theydo not perform well and tend to remove the image details. Inresponse to these difficulties, modified median filters, suchas weighted median filter (WMF), center weighted medianfilter (CWMF), and multistate median filter,35 are intro-duced. However, most of the median-based filters are oper-ated uniformly across the image and thus tend to alter bothnoisy and noise-free pixels and hence produce blurring onoutput images.

In order to overcome the problem of median-based filters,different kinds of decision-based median filters, such asprogressive switching median filter (PSMF)6 and adaptivemedian filter (AMF),7 have been proposed. Since theAMF uses larger window size and PSMF uses larger num-bers of iterations to detect the presence of noise, their com-putation time is also very high. In addition to that, switchingstrategies used in certain switching-based median filters

cannot differentiate high-frequency edges from high-fre-quency impulses in a noisy image.

Hence, to recover edges satisfactorily by taking intoaccount the local features, a SMF incorporated with powerfulnoise detection method called boundary discriminative noisedetection (BDND) is proposed.8 In this algorithm, two iter-ations are invoked to detect and validate the category of cur-rent pixel as noisy or noise-free. The pixels detected as noisyare then restored with noise adaptive switching median(NASM)9 filter. Though BDND filter provides accuratenoise detection, it is time consuming due to a larger number

of pixels being processed to detect the presence of noise. Inaddition to that, it reduces the blurring effect at higher noisedensity due to larger filtering window.

In order to overcome the complexity of different switch-ing-based median filters, a new decision-based algorithm(DBA) is proposed,10 which uses the fixed window with asize of 3 3 for image denoising. If the center pixel ofthe sliding window is either 0 or 255, it is replacedwith median value otherwise retained. At higher noise levels,all the pixels in the selected window are corrupted, and themedian value may also be a noisy value, in which the pre-viously processed left neighborhood pixel is used to replacethe corrupted center pixel that produces streaking effect.

To address this issue, decision-based unsymmetric

trimmed median filter (DBUTMF) has been proposed.11In this filter, at higher noise levels, the trimmed medianvalue cannot be obtained if the selected window contains allthe pixels as noisy pixels. In addition to that, DBUTMF doesnot provide better restoration results at higher noise ratios. Toovercome the above drawback, the modified decision-basedunsymmetric trimmed median filter (MDBUTMF) has beenproposed, which takes the mean of all the pixels in a selectedwindow to replace the noisy center pixel.12 Since this filter

*Address all correspondence to: Vaithiyam Rengarajan Vijaykumar, E-mail:[email protected] 0091-3286/2014/$25.00 2014 SPIE and IS&T

Journal of Electronic Imaging 033011-1 MayJun 2014 Vol. 23(3)

Journal of Electronic Imaging 23(3), 033011 (MayJun 2014)

http://dx.doi.org/10.1117/1.JEI.23.3.033011http://dx.doi.org/10.1117/1.JEI.23.3.033011http://dx.doi.org/10.1117/1.JEI.23.3.033011http://dx.doi.org/10.1117/1.JEI.23.3.033011http://dx.doi.org/10.1117/1.JEI.23.3.033011http://dx.doi.org/10.1117/1.JEI.23.3.033011http://dx.doi.org/10.1117/1.JEI.23.3.033011


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detects the presence of salt-and-pepper noise by maximum-intensity value 255 and minimum-intensity value 0, thedetection accuracy is not enough to restore the images cor-rupted with more than 80% of noise level. In addition tothat, if all the pixels in the window are either 0 or 255,then the MDBUTMF replaces the noisy pixel by mean value,which is also either 0 or 255. Unlike the median filter,mean filters smooth the images. Recently, an improved BDND

filter13

is proposed to overcome the blurring effect of BDNDby considering the spatial correlation between the noisy anduncorrupted pixels in the filtering window. Though it reducesthe blurring effect, the computation time is still high since ituses the same detection process as in BDND.

To overcome the above drawbacks in various filters, a newdecision-based trimmed median filter, to remove high-den-sity salt-and-pepper noise with better performance interms of qualitative and quantitative results, is proposed inthis paper. In the proposed filter, a fixed 3 3 sliding win-dow is applied to the current pixel being processed, and thepixels are sorted. A trimmed array is obtained by eliminatingthe minimum- and maximum-intensity values in the sortedarray. The noisy pixels are detected by comparing the abso-

lute difference between the center pixel and the median valueof uncorrupted pixels in the trimmed array with a predefinedthreshold value T. If it is identified as noisy pixel, then itis replaced with the median value otherwise left unaltered.The rest of this paper is organized as follows. In Sec. 2,the proposed trimmed median filtering algorithm isdescribed and illustration is given in Sec.3. The simulationresults of the proposed trimmed median filter in imagedenoising application and performance comparisons withthe other existing algorithms are displayed in Sec. 4.Section5 concludes the paper.

2 Proposed Decision-Based Trimmed Median Filter

Initially, a 3 3 fixed sliding window is imposed on eachpixel being processed in the noisy image. The minimum-intensity (Smin) and maximum-intensity (Smax) valuesobtained in the selected window are trimmed, and remainingpixels, which are not equal to Sminand Smax, are collected inan array. Then, the absolute difference between the centerpixel and the mean value of those pixels collected in thearray is compared with a predefined threshold value Tto detect whether the center pixel is corrupted or not. If itis detected as noisy pixel, then filtering is applied; otherwiseit is left unaltered. Because of the detection mechanism, theproposed algorithm works well even above the 50% break-down limit for a3 3fixed window. In the case of 90% andabove noise levels, if all the pixels in the 3 3filtering win-dow are corrupted, then the proposed algorithm replaces the

center pixel with the midpoint of previously processed fourpixels. The proposed algorithm is explained in the followingsteps.

Algorithm Steps:

Step 1: Let Xij be a pixel being processed in the noisyimage. A 3 3 fixed window W3i; j defined inEq. (1) centered aboutXij is applied, and elements inW3i; j are collected in an array Ziji19. Smin andSmaxin the window are obtained by sorting the elementsin the array Zi

W3i; j Xik; jl; 1 k; l 1: (1)

Case (i)

Step 2: If Smin 0 and Smax 255 continue; else go toStep 6.

Step 3: TheSminand Smaxvalues in the arrayZiare trimmed

and all the uncorrupted pixels, which are not equal toSmin and Smax, are retained in the same array. The setof noise-free coordinates are defined in Eq. (2), inwhich fik;jl is gray level intensity at pixel locationik, jl. If Zi is empty go to Step 11; elsecontinue.

Si;j fik:j1; ik; j1

W3i; j fik;j1 Smin fik;j1Smaxg

(2)

Step 4: Median (MED) of an array Zi is found. IfjXij MEDj< T, then Xij is noise-free and actual

value is retained; otherwise Xij is replaced with MED,in which the threshold value T lies in the range[2730].

Step 5: Repeat the process from Step 1, until all the pixels inthe noisy image are processed.

Case (ii)


Step 7: TheSminand Smaxvalues in the arrayZiare trimmedand all the uncorrupted pixels, which are not equal toSmin, in trimmed array Zi are retained. The set ofnoise-free coordinates are defined by Eq. (3), inwhich fik;jl is gray level intensity at pixel location

ik, jl. If Zi is empty go to Step 11; else goto Step 4.

Si;j fik; j1; ik; j1

W3i; j fik;j1 Sming: (3)

Case (iii)


Step 9: TheSminand Smaxvalues in the arrayZiare trimmedand all the uncorrupted pixels, which are not equal toSmax, in trimmed array Zi are retained. The set ofnoise-free coordinates is defined by Eq. (4), in whichfik;jl is gray level intensity at pixel location ik,jl. If Zi is empty go to Step 11; else go toStep 4.

Si;j fik; j1; ik; j1

W3i; j fik;j1 Smaxg: (4)

Step 10: The current processing pixelXij is noise-free andactual value is retained.


Vijaykumar and Santhanamari: New decision-based trimmed median filter for high-density salt.. .



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Step 11: The midpoint of previously processed neighborsXi1;j1, Xi1;j Xi1;j1, Xi;j1 is used to replace thecenter pixel Xij and go to Step 5.

In the case of 90% and above noise density, if there is nouncorrupted pixel in the trimmed array Zi, the mean ormedian statistics can also be used to replace the corruptedcenter pixel instead of midpoint estimator as explained in

Step 11. Nevertheless, there is not much difference amongmean, median, and midpoint estimators; the computationtime for obtaining midpoint of previously processed four

pixels is less compared to mean and median estimators.Hence, midpoint statistics are chosen in the proposed algo-rithm. The optimum threshold value T is determined bytrial-and-error approach for various test images and liesapproximately in the range [2730].

3 Illustration of Proposed Filter

This section illustrates the proposed algorithm with four dif-ferent cases for Lena image corrupted with 70% of salt-and-pepper noise.

Table 1 Peak signal-to-noise ratio (PSNR) comparison for Lena and Bridge image.

ND (%)

Lena Bridge

SMF WMF CWMF PSMF AMF DBA MDBUTMF Proposed SMF WMF CWMF PSMF AMF DBA MDBUTMF Proposed

10 33.76 34.27 3 3.62 38.72 38.01 38.06 41.15 39.26 26.16 27.54 2 7.63 35.22 29.59 29.34 31.16 28.31

20 29.49 27.14 2 5.29 36.20 34.97 37.23 37.25 37.27 24.40 24.37 2 3.44 32.77 28.15 28.21 28.55 27.58

30 24.01 21.46 2 0.02 35.39 32.37 35.68 34.75 35.67 21.40 20.07 1 9.08 30.71 26.78 26.98 26.64 26.96

40 19.17 17.21 1 6.14 35.09 29.96 33.76 32.26 34.47 18.07 16.56 1 5.52 29.49 25.35 25.68 25.08 26.29

50 15.35 14.04 1 3.11 34.36 28.26 31.65 30.27 33.11 14.76 13.43 1 2.67 28.40 23.89 24.36 23.53 25.53

60 12.32 11.51 10.8 32.15 26.64 30.10 28.03 31.51 11.86 11.20 10.52 27.25 22.51 23.02 21.85 24.58

70 10.07 9.45 9.05 27.45 24.67 28.20 25.75 29.73 9.77 9.18 8.79 24.57 21.09 21.92 20.16 23.43

80 8.14 7.86 7.56 20.60 21.37 25.75 22.81 27.74 7.85 7.61 7.37 19.32 18.17 20.55 18.20 22.00

90 6.6 6.51 6.36 14.39 14.43 23.14 18.14 24.48 6.42 6.32 6.19 13.79 13.51 18.78 15.45 20.00

Table 2 Mean absolute error (MAE) and image enhancement factor (IEF) for Lena image.

ND (%)

MAE IEF


10 1.442 1.109 0 .913 0.923 0.968 0.973 0.172 0.255 22.83 37.51 5 6.04 248.0 230.3 236.6 623.97 672.2

20 1.773 1.593 1 .650 1.707 1.313 1.281 0.374 0.449 53.98 60.25 5 8.56 312.0 200.0 339.6 546.08 761.9

30 2.510 2.906 3 .347 2.230 1.801 1.760 0.594 0.661 51.33 37.12 3 1.23 400.6 94.11 368.8 472.18 760.9

40 4.460 5.445 6 .570 2.619 2.513 2.366 0.883 0.866 30.29 18.96 1 4.09 467.5 50.97 321.1 391.03 733.2

50 8.224 10.10 1 1.84 3.086 3.309 3.214 1.210 1.126 14.02 9.167 6 .721 494.5 32.97 263.9 307.31 687.3

60 14.52 16.86 1 9.04 4.183 4.309 4.124 1.661 1.462 6.630 4.924 3 .700 359.6 26.28 205.3 239.86 625.3

70 23.18 25.95 2 7.98 7.188 5.753 5.439 2.257 1.858 3.554 2.841 2 .380 116.0 18.12 152.0 164.66 519.0

80 34.60 36.64 3 8.77 20.22 8.541 7.614 3.310 2.501 2.068 1.854 1 .640 13.37 12.53 102.7 90.632 422.6

90 48.17 45.50 4 9.80 68.34 21.95 12.79 5.970 3.896 1.357 1.289 1 .250 1.232 5.227 54.25 24.676 272.7





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Case (i)The case if the center pixel in the selected window is noisy and some neighborhood pixels add salt-and-pepper noise to the image

is illustrated in case (i). The pixels in the selected window are sorted, and Sminand Smaxvalues are trimmed. Then, the uncorruptedpixels, which are not equal to Smin andSmax in Zi, are retained. The median value of the array Zi is found. Since the absolutedifference between the median value and the center pixel value is greater than 30, the center pixel is noisy and replaced with themedian value as shown below:

0 49 50 Trimmed array Zi= [0, 46, 48, 49, 50, 255, 255]

0 255 255 Zi= [46, 48, 49, 50] MED = 49

46 255 48 X| |ij MED = 206 > 30, Xij= 49

Table 3 Mean absolute error (MAE) and image enhancement factor (IEF) for Bridge image.

ND (%)

MAE IEF


10 3.709 2.788 2 .321 1.656 2.777 2.947 0.482 1.410 3.865 7.120 9 .978 56.96 41.01 52.58 48.28 25.21

20 4.213 3.423 3 .175 3.125 3.436 3.543 0.991 1.824 11.39 16.35 1 8.78 65.00 87.91 133.5 62.80 55.64

30 5.207 4.880 4 .942 5.005 4.392 4.436 1.576 2.257 16.15 16.58 1 4.84 56.91 99.55 204.7 67.90 82.99

40 7.082 7.340 7 .994 6.630 5.705 5.674 2.220 2.723 14.14 11.38 9 .062 52.24 74.49 275.1 65.54 97.54

50 10.45 11.84 1 3.05 8.539 7.320 7.186 3.025 3.228 8.935 6.600 5 .252 49.18 58.83 291.5 55.65 106.0

60 16.13 17.26 1 8.97 10.76 9.283 9.090 3.929 3.917 4.982 3.994 3 .235 46.51 34.72 298.1 46.19 107.0

70 23.43 25.30 2 7.01 14.93 11.76 11.21 5.154 4.766 3.054 2.520 2 .182 26.76 26.42 240.9 35.62 99.67

80 33.46 34.69 3 6.08 29.57 15.93 14.06 7.023 5.940 1.903 1.737 1 .585 8.104 18.35 157.6 24.89 86.02

90 44.99 45.48 4 6.13 76.57 30.12 18.62 9.754 7.953 1.342 1.281 1 .209 1.113 7.251 78.76 11.21 61.82

Table 4 Structural similarity index (SSIM) for Lena and Bridge image.

ND (%)

Lena Bridge


10 0.911 0.930 0 .934 0.907 0.962 0.964 0.990 0.995 0.780 0.850 0 .867 0.903 0.911 0.910 0.976 0.924

20 0.862 0.839 0 .788 0.878 0.953 0.957 0.978 0.976 0.733 0.773 0 .764 0.886 0.894 0.895 0.950 0.894

30 0.718 0.623 0 .525 0.891 0.939 0.940 0.965 0.963 0.629 0.619 0 .574 0.834 0.866 0.859 0.917 0.875

40 0.468 0.359 0 .282 0.902 0.916 0.921 0.947 0.949 0.468 0.423 0 .360 0.789 0.823 0.820 0.877 0.846

50 0.238 0.177 0 .129 0.905 0.889 0.887 0.924 0.931 0.284 0.242 0 .201 0.731 0.769 0.766 0.820 0.812

60 0.109 0.085 0 .065 0.872 0.854 0.836 0.891 0.908 0.148 0.138 0 .111 0.661 0.704 0.701 0.751 0.768

70 0.052 0.042 0 .036 0.769 0.802 0.774 0.845 0.877 0.080 0.071 0 .059 0.550 0.621 0.632 0.653 0.709

80 0.025 0.022 0 .018 0.467 0.692 0.691 0.769 0.835 0.037 0.037 0 .030 0.326 0.491 0.529 0.514 0.629

90 0.011 0.011 0 .009 0.091 0.338 0.537 0.622 0.759 0.015 0.017 0 .015 0.077 0.249 0.384 0.333 0.492





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Case (ii)The case if the center pixel in the selected window is noisy and some neighborhood pixels add pepper noise to the image is

illustrated in case (ii). Since the absolute difference between the median value of the array Zi and center pixel value is greaterthan 30, the center pixel is noisy and replaced with the median value as shown below:

| |

0 205 206 Trimmed array Zi= [0, 0, 205,205,205,206,208]

205 0 209 Zi= [205, 205, 205, 206, 208] MED = 205

0 208 205 Xij MED = 205 > 30, Xij= 205

Fig. 1 Comparison of (a) PSNR, (b) MAE, (c) IEF, (d) SSIM, (e) run time of various algorithms for Lenaimage corrupted with various noise densities.





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Case (iii)The case if the center pixel in the selected window is noisy and some neighborhood pixels add salt noise to the image is

illustrated in case (iii). Since the absolute difference between the median value of the arrayZi and center pixel value is greaterthan 30, the center pixel is noisy and replaced with the median value.

255 49 57 Trimmed array Zi= [49, 50, 51, 52, 57, 255, 255]

51 255 50 Zi= [49, 50, 51, 52, 57] MED = 51

52 255 48 X| |ij MED = 204 > 30, Xij= 51

Fig. 2 (a)(j) Restoration results for Lena image corrupted with 95% salt-and-pepper noise density.(a) Original, (b)noisy, (c)SMF, (d)WMF, (e) CWMF, (f) PSMF, (g)AMF, (h)DBA, (i) MDBUTMF, (j) proposed.





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Case (iv)If the center pixel value is noise free, then the absolute difference between the median value and center pixel is less than 30,

then the processing pixel is left unaltered.

| |

| |

58 66 56 Xij MED = 0 < 30, Xij= 59

73 59 65 Zi = [57, 57, 58, 59, 63, 65, 66] MED=59

58 66 56 Xij MED = 0 < 30, X

ij= 59

Fig. 3 (a)(j) Restoration results for bridge image corrupted with 80% salt-and-pepper noise density.(a) Original, (b)noisy, (c)SMF, (d)WMF, (e) CWMF, (f) PSMF, (g)AMF, (h)DBA, (i) MDBUTMF, (j) proposed.





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4 Results and Discussion

In this section, the performance of the proposed filter istested by using standard grayscale test images namelyLena, Bridge, Elaine, and Peppers of size 512 512,8 bitspixel and compared with state-of-the-art algorithms,such as SMF, WMF, CWMF, PSMF, AMF, DBA andMDBUTMF, by varying the noise level from 10% to 90%with the incremental step of 10% for every simulation. In

addition to the visual quality, the performance of theproposed algorithm and the other existing algorithms isquantitatively measured by the parameters such as peak sig-nal-to-noise ratio (PSNR), mean absolute error (MAE),structural similarity index (SSIM), and image enhancementfactor (IEF). The performance of restoration and processingtime for proposed filter and the existing filters are analyzedunder the following Secs. 4.1and4.2.

Fig. 4 (a)(j) Restoration results for Elaine image corrupted with 70% salt-and-pepper noise density.(a) Original, (b) noisy, (c) SMF, (d) WMF, (e) CWMF, (f) PSMF, (g) AMF, (h) DBA, (i) MDBUTMF,(j) proposed.





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4.1 Quantitative and Visual Results Comparison

The restoration performance of the proposed algorithm isdemonstrated in this section. The quantitative performancemetrics, in terms of PSNR, MAE, IEF, and SSIM for pro-posed filter and seven competitive filters for the test imagesLena and Bridge at noise level varying from 10% to 90%, aredocumented in Tables 14.

The performance of SMF, WMF, and CWMF in terms of

visual and quantitative metrics is poor compared to the

proposed and the other existing filters for low to highnoise densities since there is no noise detection processinvolved. Though the PSNR value obtained by the PSMFalgorithm is equally as good as the proposed filter fornoise densities up to 60%, it decays to very low value forhigher noise densities. The AMF algorithm produces betterPSNR up to a noise density level of 40%, and it decreases athigher noise densities due to larger window size. The fixed

window algorithms, such as DBA and MDBUTMF, produce

Fig. 5 (a)(j) Restoration results for Peppers image corrupted with 60% salt-and-pepper noise density.(a) Original, (b) noisy, (c) SMF, (d) WMF, (e) CWMF, (f) PSMF, (g) AMF, (h) DBA, (i) MDBUTMF,(j) proposed.





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Fig. 6 (a)-(j) Restoration results for gray level variation of 100th row of Lena image corrupted with 90%noise density. (a) Original, (b) noisy, (c) SMF, (d) WMF, (e) CWMF, (f) PSMF, (g) AMF, (h) DBA,(i) MDBUTMF, (j) proposed.





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lower PSNR values than the proposed filter for noise levelmore than 60%.

The proposed algorithm produces much lower MAE andbetter IEF than the existing filters at higher noise densities,which are given in Tables 2 and 3. The proposed algorithmalso exhibits improved structural similarity index, whichis displayed in Table 4. The above discussed quantitativeperformance comparisons are also presented graphically

in Fig. 1.

The proposed algorithm is analyzed qualitatively byobserving the restoration result of proposed algorithm andthe existing algorithms, for the images Lena corruptedwith 95% of salt-and-pepper noise and Bridge corruptedwith 80% salt-and-pepper noise, visually shown in Figs. 2and 3, respectively. The algorithms, such as SMF, WMF,and CWMF, failed to restore the original image for thenoise level greater than 50%, and PSMF leaves some notice-

able impulses in the output image at higher noise densities.

Fig. 7 (a)(j) Error images for Lena image corrupted with 90% salt-and-pepper noise density.(a) Original, (b) noisy, (c) SMF, (d) WMF, (e) CWMF, (f) PSMF, (g) AMF, (h) DBA, (i) MDBUTMF,(j) proposed.





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At higher noise densities, DBA produces a streaking effectdue to the repeated replacement of left neighborhood pixel inthe sliding window. The AMF restores the original imagewith slight blurring effect, because of the larger windowsize. Figures 4 and 5 show the restoration results ofvarious filters for Elaine image corrupted with 70% salt-and-pepper noise and the Peppers image corrupted with60% salt-and-pepper noise, respectively. Based on the sub-

jective visual comparisons, it is also observed that the pro-posed filter removes impulse noise effectively and preservesthe image details, such as edges, better than the other existingfilters.

The change in intensity profile for a single row of origi-nal, noisy, and restored image for various filters is shown inFig.6. It can be seen from the figure that the intensity varia-tion of the original and restored image remains almost samefor the proposed filter than the existing filters. The errorimage of proposed and the other existing filters for Lena cor-rupted with 90% salt-and-pepper noise density is displayedin Fig.7. The error image for the proposed filter looks darkerthan other competitive filters, which clearly show the betteredge preservation. Based on the above analysis, it is easy to

see that the proposed filter outperforms the existing switch-ing-based filters in both quantitative and qualitative aspects.In order to show the visual performance of the proposedalgorithm and the other existing algorithms more clearly,all four test images are corrupted with 90% salt-and-peppernoise density, and restoration results are presented in Fig.8.The visual results in Fig.8 clearly indicate the superior per-formance of the proposed algorithm over the existingmethods.

4.2 Run-Time Comparison

In addition to PSNR, MAE, and MSSIM, the performanceof proposed filter is also tested quantitatively in terms of

processing time and compared with the existing filters fortest images, such as Lena, Bridge, Elaine, and Peppers,with noise level varying from 10% to 90% and listed inTables 5 and 6. All the filters are simulated in MATLABon a PC equipped with 2.66 GHz operating speed, 2GBRAM. The computation time for SMF, WMF, and CWMFis much less because there is no detection mechanisminvolved.

From Tables 5 and 6, it is observed that the PSMFalgorithm has taken longer run time than the proposedalgorithm due to processing of more pixels in an iterativemanner. The AMF is executed with longer time than theproposed filter, especially at higher noise densities, sinceit uses a large window size for a higher noise ratio. The

run time for MDBUTMF is less only at lower noise levelsand it takes more time for execution than the proposedfilter at higher noise densities above 70%. It is also inferredfrom the tables that the fixed window algorithm DBA hastaken a run time much closer to the proposed filter for noiselevels varying from 10% to 90%, but a streaking effectdominates in DBA at higher noise ratios. Hence, the pro-posed filter provides a better tradeoff among run timeand other performance metrics, such as PSNR, and visualquality than the existing algorithms, especially at highernoise levels.

Fig. 8 Restoration results of (a) Lena, (b) Bridge, (c) Elaine and(d) Peppers images using various filters, namely SMF, WMF, CWMF,PSMF, AMF, DBA, MDBUTMF, andproposedalgorithm, for 90%salt-and-pepper noise densities.





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5 Conclusion

In this paper, a new decision-based trimmed median filterwith fixed window for effective removal of high-densitysalt-and-pepper noise in images is proposed. The use of asmall 3 3 fixed window in the proposed algorithm leadsto preservation of fine details, such as edges, satisfactorily.The better noise-removal capability of the proposed filterover other fixed window algorithms, such as DBA andMDBUTMF, is demonstrated using different test images.Experimental results reveal that the proposed filter outper-forms the existing state-of-the-art filters by providing better

PSNR, IEF, SSIM, MAE values and visual quality for theimages corrupted up to 95% of noise level.

References

1. R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed.,Prentice Hall, Upper Saddle River, NJ (2002).

2. I. Pitas and A. N. Venetsanopoulos, Order statistics in digital imageprocessing, Proc. IEEE, 80(12), 18931921 (1992).

3. L. Yin et al., Weighted median filters: a tutorial,IEEE Trans. CircuitsSyst. II: Analog Digital Signal Process. 43(3) 157192 (1996).

4. S. J. Ko Chen and Y. Hoom Lee, Center-weighted median filters andtheir applications to image enhancement, IEEE Trans. Circuits Syst.38(9), 984993 (1991).

Table 5 Run time comparison for Lena and Bridge image.

ND (%)

Lena Bridge


10 5.49 6.04 5.65 38.85 7.12 6.51 1.62 7.44 5.5 6.04 5.65 36.75 7.46 6.56 1.60 7.41

20 5.53 6.06 5.68 36.59 7.13 6.54 2.57 7.45 5.54 6.04 5.70 37.01 7.42 6.53 2.59 7.48

30 5.51 6.03 5.62 36.75 7.14 6.50 3.48 7.48 5.51 6.04 5.67 36.62 7.45 6.51 3.56 7.51

40 5.48 6.09 5.71 36.87 7.37 6.54 4.39 7.49 5.48 6.03 5.70 36.68 7.61 6.60 4.43 7.54

50 5.51 6.04 5.70 36.91 7.85 6.51 6.89 7.51 5.51 6.04 5.67 36.78 8.06 6.56 5.32 7.48

60 5.50 6.03 5.75 36.65 8.70 6.56 7.73 7.51 5.50 6.04 5.73 36.73 9.42 6.51 6.23 7.45

70 5.53 6.04 5.69 36.95 10.21 6.53 8.48 7.48 5.53 6.03 5.68 37.01 10.5 6.53 7.09 7.46

80 5.53 6.04 5.70 37.59 13.63 6.50 9.31 7.48 5.53 6.03 5.7 37.82 13.6 6.51 7.98 7.42

90 5.53 6.03 5.70 38.75 20.42 6.54 10.15 7.37 5.53 6.06 5.71 38.96 20.7 6.54 8.78 7.39

Table 6 Run time comparison for Elaine and Pepper image.

ND (%)

Elaine Peppers


10 5.54 6.07 5.71 37.26 7.11 6.58 1.57 7.45 5.57 6.12 5.71 38.67 7.14 6.55 1.57 7.45

20 5.56 6.09 5.70 36.38 7.12 6.61 2.54 7.46 5.50 6.07 5.70 36.9 7.25 6.74 2.53 7.46

30 5.57 6.07 5.71 36.86 7.10 6.58 3.48 7.51 5.53 6.09 5.73 37.02 7.18 6.68 3.48 7.48

40 5.56 6.06 5.71 36.73 7.45 6.59 4.42 7.48 5.54 6.07 5.68 36.95 7.51 6.71 4.39 7.5

50 5.56 6.09 5.75 36.94 8.01 6.57 5.34 7.42 5.56 6.07 5.71 36.99 7.85 6.90 5.34 7.53

60 5.53 6.12 5.76 35.94 8.85 6.54 6.25 7.51 5.56 6.07 5.75 37.11 8.89 6.54 6.23 7.5

70 5.56 6.09 5.76 37.88 10.02 6.58 8.54 7.48 5.59 6.09 5.71 37.53 10.630 6.54 8.53 7.54

80 5.53 6.10 5.76 37.54 13.14 6.57 8.10 7.48 5.56 6.09 5.68 37.74 13.48 6.61 9.39 7.65

90 5.53 6.06 5.71 39.01 19.63 6.56 10.2 7.42 5.56 6.06 5.71 37.93 19.41 6.71 10.23 7.65



http://dx.doi.org/10.1109/5.192071http://dx.doi.org/10.1109/82.486465http://dx.doi.org/10.1109/82.486465http://dx.doi.org/10.1109/31.83870http://dx.doi.org/10.1109/31.83870http://dx.doi.org/10.1109/82.486465http://dx.doi.org/10.1109/82.486465http://dx.doi.org/10.1109/5.192071


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Vaithiyam Rengarajan Vijaykumar received his BE degree in elec-tronics and communication engineering from Madras University, andhis ME degree in communication systems at Thiagarajar College ofEngineering Madurai in 1997. He completed his PhD degree in thearea of nonlinear image filtering from Anna University in 2008. Hehas 17 years of teaching experience. He has worked at Madras

Institute of Technology, Chennai, and PSG College of Technologyas a teaching faculty. Currently, he is working as associate professorin the Department of Electronics and Communication Engineering,Anna University, Coimbatore, TamilNadu, India. His areas of interestinclude image processing, signal processing, and digitalcommunication.

Guru Santhanamari is currently working as an assistant professor(senior grade) in the Department of Electronics and CommunicationEngineering, TamilNadu College of Engineering, Coimbatore, India.She received her BS degree in Government College of Technology,Coimbatore, and MS degree in PSG College of Technology, Coimba-tore. Her research interests include digital image processing, signalprocessing, and embedded systems.

Jo rnal of Electronic Imaging 033011 14 Ma J n 2014 Vol 23(3)

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Median Filter for High-Density Salt-And-pepper Noise Removal in Images

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