Denoising of salt-and-pepper noise corrupted image using modified directional-weighted-median filter

pt OC s ha a h ch t ente e on ncha image. � 2012 Elsevier B.V. All rights reserved. ent du al acq re salt er no ther m tly de median filter is that the filter is only effective to work at low noise densities. This is due to the filter uniformly replaces the value of the center pixel by the median value of a local window. Accord- ingly, some desirable details were also replaced, especially when the window size was large, yielding the restored image being blurred. A switching median filter (Sun and Neuvo, 1994) parti- the neighbor information of the center pixel on four directions to weight the pixels in a local window. A noise-corrupted pixel could be detected, and hence removed by the weighted median filter on the optimum direction. Experimental results showed that this method could be employed to remove random-valued impulse noise in a noisy image, when the noise density was as high as 60%. Based on the above findings, how to improve the switch- median filter (Zhang and Karim, 2002; Bovik, 2000) to cope with a heavy noise corrupted image (noise density exceeds 60%) is a challenging research task. Although the DWM filter (Dong and Xu, 2007) can efficiently denoise a noisy image under slight noise ⇑ Corresponding author. Address: Department of Information Communication, Asia University, 500, Lioufeng Rd., Wufeng, Taichung 41354, Taiwan, ROC. Tel.: +886 4 23323456x1869; fax: +886 4 23305824. Pattern Recognition Letters 33 (2012) 1287–1295 Contents lists available at Pattern Recogn .e l E-mail address: [email protected] (C.-T. Lu). an image. How to efficiently remove this kind of impulse noise is an important research task. Many nonlinear filters have been proposed for the restoration of images contaminated by salt-and-pepper noise (Chen et al., 1999; Chan et al., 1999; Chen and Lien, 2008; Akkoul et al., 2010; Toh and Isa, 2010; Wan et al., 2010; Duan and Zhang, 2010; Hwang and Hadded, 1995; Sun and Neuvo, 1994; Zhang and Karim, 2002). Most of these standard median filters have been established as a reliable method to remove salt-and-pepper noise without damag- ing the edge details. However, the major drawback of standard size has to be increased which may lead to blur in the denoised im- age. In the modified switching median filters (Zhang and Karim, 2002; Bovik, 2000), the decision of an impulse noise pixel was based on a pre-defined threshold value. The major drawback of these methods is that defining a robust decision threshold is diffi- cult. Also these filters did not take into account the local features as a result of which details and edges could not be recovered satisfac- torily, especially when noise density was high. A directional- weighted-median (DWM) filter (Dong and Xu, 2007) was proposed for removing random-valued impulse noise. This method analyzed Median filter Motion direction Iterative filtering 1. Introduction Impulse noise in an image is pres mission or introduced during the sign two types of impulse noise, they a random valued noise. Salt-and-pepp where the corrupted pixel takes ei gray level. This noise can significan 0167-8655/$ - see front matter � 2012 Elsevier B.V. A http://dx.doi.org/10.1016/j.patrec.2012.03.025 e to bit errors in trans- uisition stage. There are -and-pepper noise and ise can corrupt images aximum or minimum teriorate the quality of tioned the whole filtering process into two sequential steps which includes noise detection and filtering, where the noise corrupted pixels were filtered by the median filter. On the contrary, noise- free pixels were kept unchanged to maintain image quality. When noise density exceeds 50% in an image, the edge details of the original image cannot be preserved by standard median filter. An adaptive median filter (Hwang and Hadded, 1995) performed well at low noise densities. But at high noise densities the window Image denoising Salt-and-pepper noise image being well maintained. Experimental results show that the proposed approach cannot only effi- ciently suppress high-density impulse noise, but also can well preserve the detailed information of an Denoising of salt-and-pepper noise corru directional-weighted-median filter Ching-Ta Lu ⇑, Tzu-Chun Chou Department of Information Communication, Asia University, Taichung 41354, Taiwan, R a r t i c l e i n f o Article history: Received 22 October 2011 Available online 5 April 2012 Communicated by Jie Zou Keywords: a b s t r a c t Many denoising algorithm them cannot well recover we propose a new approa pixels in an image. If the c by a weighted median valu the center pixel is kept u journal homepage: www ll rights reserved. ed image using modified ve been proposed to recover a noise corrupted image. However, most of eavy noise corrupted image with noise density above 70%. In this Letter, o efficiently remove background noise by detecting and modifying noisy r pixel of a local window is classified to noisy, this center pixel is replaced an optimum direction, enabling impulse noise to be removed. Conversely, nged when it is classified to noise-free, yielding the quality of restored SciVerse ScienceDirect ition Letters sevier .com/locate /patrec corruption, this filter fails to enhance a heavy noise-corrupted im- age (noise density above 70%). In this Letter, we propose improving the performance of the DWM filter by finding a better edge direc- tion and giving an additional constraint on performing switch median filtering. Experimental results show that the proposed method can significantly improve the performance of the DWM fil- ter in removing much more quantity of background noise, while the details of the original image are well preserved. In addition, the proposed approach can also well perform in enhancing a noisy image with noise density up to 90%. The rest of this Letter is organized as follows. Section 2 de- scribes the proposed modified directional median filter. Section 3 demonstrates the experimental results. Conclusions are finally drawn in Section 4. 2. Proposed approach The block diagram of proposed method is shown in Fig. 1. Ini- tially, a noise-corrupted image is analyzed by a 7 � 7 sliding win- dow. If the value of the center pixel in a local window is not an extreme value (0 or 255), the center pixel is classified to noise-free and kept unchanged to maintain image quality. Conversely, the center pixel needs to be further classified to which it is a noise pix- el or one of an edge pixel. If the center pixel belongs to an edge, this pixel is still kept unchanged. On the contrary, it is a noise pixel and should be modified by the directional-weighted-median (DWM) filter. The pixels with extreme value (0 or 255) should be excluded before taking the DWM filtering, enabling the salt-and-pepper noise to be thoroughly removed. The local window slides from left-hand side to right-hand one, and slides from the upper-left 1288 C.-T. Lu, T.-C. Chou / Pattern Recogniti Fig. 1. Block diagram of proposed modified directional weighted median filter. corner to the bottom-right one in an image until all pixels have been processed. In order to ensure impulse noise can be efficiently removed, the procedures including noise detection and the modi- fied DWM filtering are iteratively performed until attaining a pre- set iteration number. A denoised image is accordingly obtained. 2.1. Impulse noise detection A noise-free image consists of smoothly varying areas separated by edges in a local window. Dong and Xu (2007) proposed using four directions to find the edge of an object. Here we propose employing twelve directions to detect the edge direction of an ob- ject, enabling the detection accuracy to be improved. Fig. 2 shows the twelve directions for edge detection, where the center pixel is represented in filled circle. As shown in Fig. 2, a 7 � 7 window centered at (i, j), for each direction, we can compute the absolute differences of gray-level values dðkÞi;j between the center pixel xi,j and its neighbors xi+Di,j+Dj for noise detection. The difference can be computed by dðkÞi;j ¼ P Di P Dj wDi;Dj � jxiþDi;jþDj � xi;jj ð1Þ where k denotes the direction index, with 1 6 k 6 12. wDi,Dj is the weight of the neighbor pixel with offset Di on horizontal direction and offset Dj on vertical direction from the center pixel. Considering a pixel adjacent to the center one, the gray-level value should be close when they are the edge of an object or in the same smoothly varying area. The corresponding spatial dis- tance given in (1) should be small. Thus the weight of the absolute difference between the two closest pixels has a larger value than that of the pixels which are not adjacent to the center pixel. The weights in (1) can be expressed by wDi;Dj ¼ 2; �1 6 Di;Dj 6 1 1; elsewhere � ð2Þ In order to detect the edge of an object in a given window, we select the direction with the minimum absolute difference among the twelve directions to be the optimum direction for the edge as shown in Fig. 2. The optimum direction can be achieved by k� ¼ argmin k dðkÞi;j ;1 6 k 6 12 n o ð3Þ where k⁄ denotes the index of optimum direction in a local window. The value of the absolute difference on the optimal direction dðk �Þ i;j is the smallest among the twelve directions. Hence, the value of dðk �Þ i;j can be employed to detect whether the center pixel of a lo- cal window is either noise-free or noisy. When the center pixel is noise-free in a flat variation region or on the edge of an object, the value of dðk �Þ i;j is small. Conversely, the value of d ðk�Þ i;j is large when the center pixel is impulse noise. Accordingly, we can detect an im- pulse noise pixel by the value of dðk �Þ i;j , given as xi;j 2 noise-free pixel; if d ðk�Þ i;j 6 T noisy pixel; otherwise ( ð4Þ where T is a threshold for classifying the center pixel to noise-free or noisy. If the center pixel is classified to noisy, it should be modified to remove the impulse noise. On the contrary, the center pixel has to be kept unchanged when it is classified to noise-free. 2.2. Modified directional weighting median filtering Accordingly to (4), we can decide whether the center pixel of a on Letters 33 (2012) 1287–1295 local window is noisy. If the center pixel is classified to noisy, it should be replaced by an appropriate value to remove the impulse noise. Here we employ the switch-median (SM) filter (Zhang and thoroughly. This is the other major reason why the proposed meth- od can significantly improve the performance of the DWM filter (Dong and Xu, 2007). 2.3. Iterative filtering The threshold T in (4) can dominate the performance of detect- tion, (a) directions 1–8, (b) directions 9–12. C.-T. Lu, T.-C. Chou / Pattern Recognition Letters 33 (2012) 1287–1295 1289 Karim, 2002) to recover the value of the center pixel. The value of enhanced pixel can be computed by s^i;j ¼ ai;jxi;j þ ð1� ai;jÞ�xi;j ð5Þ where s^i;j and �xi;j denote the denoised pixel and the directional- weighted-median filtered one, respectively. ai,j is a noise-free flag which can be decided according to the optimum absolute difference dðk �Þ i;j , given as ai;j ¼ 1; d ðk�Þ i;j 6 T 0; otherwise ( ð6Þ If the value of ai,j is equal to unity, the center pixel is noise-free. Substituting ai,j into (5), the restored pixel is equal to the input pix- el without change. On the contrary, the value of ai,j is equal to zero when the center pixel is classified to noisy. The center pixel is re- placed by the median value on the optimum direction k⁄. In order to improve the performance in removing a quantity of impulse noise, we exclude the extreme values 0 and 255 on the optimum direction k⁄ before taking the median filtering, given as ~xk � i;j ¼ xk � i;j ; x k� i;j – 0 and x k� i;j – 255 n o ð7Þ Hence, the center pixel which is classified to noisy is replaced by the median value on the optimum direction k⁄, given as Fig. 2. Twelve directions for edge detec �xi;j ¼ median wDi;Dj}~xk � i;j n o ð8Þ where wDi,Dj represents the weight of a pixel, its value is given in (2). } denotes the repetition operator. Since the extreme values are excluded by (7) on the optimum direction, the median value computed by (8) will not appear either 0 or 255. Thus the restored pixel can remove the impulse noise Table 1 Comparisons of restoration results in PSNR (dB) for Lena image with resolution 512 � 512. Noise density (%) Denoising method Median SM DWM Proposed 10 29.53 36.12 40.78 41.45 20 29.28 33.42 37.02 38.22 30 28.94 31.36 34.63 35.97 40 28.45 29.88 32.51 34.07 50 27.62 28.54 30.23 32.69 60 24.97 26.76 27.69 31.21 70 19.61 24.47 25.23 29.72 80 13.41 19.52 21.00 27.94 90 8.690 8.80 15.45 25.50 ing impulse noise. It is hard to decide a robust value for this thresh- old. Accordingly, we perform the modified DWM filtering iteratively with decreasing value for the threshold T. At early iter- ations, with a large threshold, impulse noise detector only identi- fies the pixels that are most likely to be noisy. In the subsequent iterations, we decrease the threshold to include more noise for modification. As suggested in Dong and Xu (2007), it has been ob- served that for 8-bits gray-level images, the following selection of the threshold always yields satisfactory results, that is Table 2 Comparisons of restoration results in PSNR (dB) for Lena image (512 � 512) with various window sizes. Noise density (%) Window size 5 � 5 7 � 7 9 � 9 10 42.28 41.45 40.85 20 38.76 38.22 37.50 30 36.45 35.97 35.35 40 34.47 34.07 33.63 50 32.98 32.69 32.19 60 31.48 31.21 30.76 70 29.96 29.72 29.44 80 28.13 27.94 27.90 90 25.40 25.50 25.41 Table 3 Comparisons of restoration results in PSNR (dB) for Boat image (512 � 512) with various window sizes. Noise density (%) Window size 5 � 5 7 � 7 9 � 9 10 39.58 38.67 37.85 20 35.99 35.36 34.56 30 33.46 33.05 32.35 40 31.68 31.34 30.75 50 30.17 29.88 29.27 60 28.57 28.32 27.87 70 27.14 26.92 26.58 80 25.19 25.13 24.94 90 22.63 22.77 22.86 Tnþ1 ¼ Tn � 0:8 ð9Þ where n denotes the number of iteration. The initial value of the threshold T0 is empirically chosen as 510. The number of iteration is selected about five to ten (Dong and Xu, 2007). 3. Experimental results Standard gray-level test images were employed to measure the performance of a denoising algorithm in the experiments. These images include ‘‘Lena’’ and ‘‘Boat’’, each with size 512 � 512. The test images were corrupted with salt-and-pepper impulse noise with various noise densities, ranges from 10% to 90%. The median filter (Bovik, 2000), the switch median filter (SM) (Zhang and Karim, 2002), and the directional-weighted-median (DWM) filter (Dong and Xu, 2007) were also implemented for comparisons. Restoration results were quantitatively measured by peak signal- to-noise ratio (PSNR) which can be expressed as (Bovik, 2000) PSNRðdBÞ ¼ 10 � log10 MAX MSE � � ð10Þ where MAX denotes the largest value of gray-level, it is 255 for an 8-bits gray-level image. The MSE represents mean-square-error be- tween original and restored images. It can by computed by 1290 C.-T. Lu, T.-C. Chou / Pattern Recognition Letters 33 (2012) 1287–1295 Fig. 3. Restored images (512 � 512) of various denoising filters for Lena image with 5 restored image using the SM filter; (d) restored image using the DWM filter; (e) restore 0% noise density. (a) Noisy image; (b) restored image using the median filter; (c) d image using the proposed method; (f) original image. MSE ¼ 1 M � N PM�1 i¼0 PN�1 j¼0 jsi;j � s^i;jj2 ð11Þ where si,j and s^i;j represent the original and the restored pixels. M and N are the sizes of an image for the width and the height, both of them are 512. Table 1 presents the performance comparisons for various im- age denoising filters in terms of the PSNR for Lena image with res- olution 512 � 512. In (10), the larger the value of the PSNR is, the better the quality of the restored image is. It can be found that the proposed filter provides the largest value of the PSNR among the four denoising filters. In the cases of slight noise corruptions, such as 10-30% noise density, the proposed method performs bet- ter than the other filters. Moreover, the proposed method signifi- cantly improves the performance of the DWM filter in heavy noise corruptions, such as noise density greater than 80%. The ma- jor reason is that the proposed method employs additional eight directions shown in Fig. 2(a) to accurately detect the variation direction of the center pixel, enabling the edge details to be well preserved. Furthermore, the pixels with extreme values (0 or 255) on the optimum direction are excluded before median filter- ing, yielding an impulse noise being efficiently removed. Tables 2 and 3 present the performance of proposed method with various window sizes. In the cases of heavy noise corruptions C.-T. Lu, T.-C. Chou / Pattern Recognition Letters 33 (2012) 1287–1295 1291 Fig. 4. Restored images (512 � 512) of various denoising filters for Lena image with 8 restored image using the SM filter; (d) restored image using the DWM filter; (e) restore 0% noise density. (a) Noisy image; (b) restored image using the median filter; (c) d image using the proposed method; (f) original image. (noise density greater than 90%), the larger the window size is, the better the performance is. It is due to the fact that most of noisy image pixels are noise. Increasing window size can include more uncorrupted pixels into an analysis window. This can prevents all pixels being excluded on the optimum direction as given in (7), yielding the restored image to be improved. Conversely, the win- dow size should be adjusted to be smaller when noise density is below 80%. It is attributed to the prevention from blur effect in denoised image. Since the performances are comparable among the images denoised by various window sizes, we propose using the window size 7 � 7 which is adequate for various noise densities. In order to explore the visual quality, we show the recon- structed images for various denoising methods with noise density equaling 50 and 80% for Lean and Boat images, respectively. Fig. 3 shows Lena image which is corrupted by salt-and-pepper noise with 50% noise density (Fig. 3(a)). It can be found that the median filter performs the worst among the four filters. Plenty of residual noise exists in the restored image, yielding the restored image being unsatisfied. The SM and the DWM filters suffer from blur effect in the restored images (Fig. 3(c) and (d)). The proposed method improves the performance of the DWM filter by reducing a quantity of salt-and-pepper noise and rendering the restored image free from blur effect, while the edges can be well preserved. 1292 C.-T. Lu, T.-C. Chou / Pattern Recognition Letters 33 (2012) 1287–1295 Fig. 5. Restored images (512 � 512) of various denoising filters for Boat image with 50% n image using the SM filter; (d) restored image using the DWM filter; (e) restored image oise density. (a) Noisy image; (b) restored image using the median filter; (c) restored using the proposed method; (f) original image. Fig. 4 shows the restored images in heavy noise corruption (80% noise density). Obviously, the median, the SM, and the DWM filters fail to restore the heavy noise corrupted image. Only the proposed method can distinguish the contour of Lena image, while the cor- rupted noise is significantly removed. Fig. 5 shows Boat image which is corrupted by salt-and-pepper noise with 50% noise density (Fig. 5(a)). There is a great quantity of residual noise in the restored image for the median filter, enabling this image to be severely deteriorated. Although the SM and the DWM filters can efficiently remove the corrupted noise, these two methods still suffer from blur effect as shown in Fig. 5(c) and (d). It can be found that the detail of the towrope on the mast and the words on the back hull of the boat are smeared. On the contrary, the corresponding details can be well restored by the pro- posed method (Fig. 5(e)). In the case of heavy noise corruption (Fig. 6(a)), the median, the SM, and the DWM filters fail to restore the heavy noise corrupted image (Fig. 6(b–d)). The contours of boats cannot be distinguished in the restored image. Conversely, the contours of boats are distinguishable for the proposed method (Fig. 6(e)). Consequently, the proposed method significantly im- proves the performance of the DWM filter not only in reducing greater quantity of corrupted noise, but also maintaining the qual- ity of a restored image at an acceptable level. This results in the re- stored image of the proposed approach being visually pleasant. C.-T. Lu, T.-C. Chou / Pattern Recognition Letters 33 (2012) 1287–1295 1293 Fig. 6. Restored images (512 � 512) of various denoising filters for Boat image with 80% n image using the SM filter; (d) restored image using the DWM filter; (e) restored image oise density. (a) Noisy image; (b) restored image using the median filter; (c) restored using the proposed method; (f) original image. Table 4 shows the performance comparisons for Lena image with resolution 256 � 256 in terms of the PSNR. It can be found that the proposed method also significantly outperforms the other three methods, especially in the cases of heavy noise corruptions (noise density greater than 70%). Fig. 7 shows an image example with resolution 256 � 256. Zelda image is corrupted by salt-and- pepper noise with noise density 80% (Fig. 7(a)). Obviously, the median (Fig. 7(b)), the SM (Fig. 7(c)), and the DWM (Fig. 7(d)) fil- ters still fail to restore the corrupted image. Only the proposed method (Fig. 7(e)) can reconstruct the contour of Zelda image. Thus the proposed method significantly outperforms the other methods. These experimental results consist with that in the resolution 512 � 512. Consequently, the proposed method can well work in various image resolutions. Fig. 7. Restored images (256 � 256) of various denoising filters for Zelda image with 8 restored image using the SM filter; (d) restored image using the DWM filter; (e) restore Table 4 Comparisons of restoration results in PSNR (dB) for Lena image with resolution 256 � 256. Noise density (%) Denoising method Median SM DWM Proposed 10 25.07 29.66 33.32 37.03 20 24.79 26.40 30.00 33.36 30 24.29 24.89 28.31 31.27 40 23.75 23.53 26.69 29.55 50 22.88 22.61 24.94 28.10 60 21.64 21.24 23.35 26.61 70 17.88 19.27 20.67 25.10 80 12.58 15.86 18.18 23.48 90 8.21 8.34 12.90 20.99 1294 C.-T. Lu, T.-C. Chou / Pattern Recognition Letters 33 (2012) 1287–1295 0% noise density. (a) Noisy image; (b) restored image using the median filter; (c) d image using the proposed method; (f) original image. 4. Conclusions An improved version of the directional-weighted-median (DWM) filter was proposed in this study. The major reason why the proposed method can significantly improve the performance of the directional-weighted-median (DWM) filter is to include additional directions (12 directions) for edge detection, where the DWM filter only employs four directions. These additional directions improve the accuracy of edge detection. In addition, a pixel with an extreme value (0 or 255 for an 8-bits gray-level im- age) were excluded before median filtering on the optimum direc- tion, yielding the impulse noise being efficiently removed, especially in the cases of heavy noise corruptions (noise density greater than 70%). Experimental results show that the proposed method performs much better than other existing denoising tech- niques in objective measures and visual quality. Acknowledgments This research was supported by the National Science Council, Taiwan, under contract number NSC 100-2221-E-468-016. The authors would like to thank the anonymous reviewers for their valuable comments which improve the quality of this article. References Akkoul, S., Ledee, R., Leconge, R., Harba, R., 2010. A new adaptive switching median filter. IEEE Signal Process. Lett. 17 (6), 587–590. Bovik, A., 2000. Handbook of Image and Video Processing. Academic Press, New York. Chan, R.H., Nikolova, C.W., Ho, M., 1999. 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Toh, K.K.V., Isa, N.A.M., 2010. Noise adaptive fuzzy switching median filter for salt- and-pepper noise reduction. IEEE Signal Process. Lett. 17 (3), 281–284. Wan, Y., Chen, Q.Q., Yang, Y., 2010. Robust impulse noise variance estimation based on image histogram. IEEE Signal Process. Lett. 17 (5), 485–488. Zhang, S., Karim, M.A., 2002. A new impulse detector for switching median filters. IEEE Signal Process. Lett. 9 (11), 360–363. C.-T. Lu, T.-C. Chou / Pattern Recognition Letters 33 (2012) 1287–1295 1295 Denoising of salt-and-pepper noise corrupted image using modified directional-weighted-median filter 1 Introduction 2 Proposed approach 2.1 Impulse noise detection 2.2 Modified directional weighting median filtering 2.3 Iterative filtering 3 Experimental results 4 Conclusions Acknowledgments References