ISBN: 978-1-4673-1601-9/12/$31.00 ©2012 IEEE 49 ICRTIT-2012

An Efficient Approach to Remove Random Valued Impulse Noise in Images

T. Veerakumar, Assistant Professor, Department of ECE,

PSG College of Technology, Coimbatore, India.

tveerakumar@yahoo.co.in

S. Esakkirajan, Assistant Professor (SG),

Department of I&CE, PSG College of Technology,

Coimbatore, India rajanesakki@yahoo.com

Ila Vennila, Associate Professor, Department of EEE,

PSG College of Technology, Coimbatore, India.

iven@eee.psgtech.ac.in

Abstract—In this paper, a new algorithm is introduced to remove the random valued impulse noise in images. This algorithm contains two stages. The first stage detects the noisy pixels in the image. In the second stage, the noisy pixel is replaced by the median value of the neighborhood noise free pixels. The absolute difference is used to detect the noisy pixel and trimmed median value replaces the noisy pixel. This proposed algorithm shows better results than the Progressive Switching Median Filter (PSM), Pixel-wise Median Absolute Difference (PWMAD), Tristate median filter (TSM), Efficient Procedure for removing Random Valued Impulse Noise (EPRIN) and Optimal Direction Based random valued impulse noise (ODRIN). The proposed algorithm is tested for different gray scale images and it gives better Peak Signal to Noise Ratio.

Keywords- Random valued impulse noise; Noise reduction; Absolute difference; Trimmed median filter;

I. INTRODUCTION Digital images are corrupted during the image acquisition

and image transmission [1]. Specifically impulse noise is caused by malfunctioning pixels in digital camera sensors, faulty memory locations in hardware, or transmission in a noisy channel. Two flavors of impulse noise are: (i) salt and pepper noise and (ii) random valued noise. In salt and pepper noise, the noisy pixels can take either 0 or 255 in the case of 8 bit gray scale image. But the random valued impulse noise can take any value between 0 and 255. For the image corrupted by salt and pepper noise, the noise detection is simple. But in random valued impulse noise, the noisy pixel varies from 0 to 255. Therefore, the noise removal algorithm must contain the noise detection and reduction stages. Impulse noise detection algorithms are weighted median [2], rank-order thresholding [3], local signal statistics [4], fuzzy reasoning [5], neural network [6], etc. The main difficulty in detection algorithm design is the optimization of the tradeoff between noise removal and edge preservation. The median filter is basically a nonlinear filter. It effectively removes impulse noise at the same time retains the edge details [7]. But, this median filter fails at above 50% noise density. So many modified median filters have been proposed to remove the impulse noise in [8]-[13]. These filters perform well on images corrupted by impulse noise at low density, but it fails on highly corrupted images.

Recently, optimal direction based algorithm was proposed to detect and remove the impulse noise [14]. In this method, optimal direction is used to find whether the pixel is noisy or not. More detail pixels can be detected if the accurate or optimal direction of the edge is determined. In this method, median value of the neighboring pixels replaces the corrupted pixel. Most of the neighborhood pixels are noisy at high noise density. This algorithm fails at high noise density (i.e), the processing noisy pixel is replaced by another noisy pixel. To overcome this drawback, we have proposed a new algorithm to estimate the noisy pixel using the absolute difference and the detected noisy pixel is replaced by trimmed median value of the neighborhood pixels.

The organization of the paper is as follows: The proposed noise detection and noise removal algorithm is given in section II. Section III deals with the illustration of the proposed algorithm. The simulation results are given in section IV. Finally, conclusions are drawn in section V.

II. DETECTION AND REDUCTION OF IMPULSE NOISE

A. Random Valued Impulse Noise The random valued impulse noise is characterized by the

Bernouli uniform noise model [1]. Let Xij be the gray level of original image (X) at (i,j) coordinate, and [Lmin, Lmax] be the dynamic range of X. Let Yij be the gray level of the noisy image Y at (i,j) coordinate, which is represented as

⎩⎨⎧

−η

=qyprobabilitwith,X

qilitywithprobab,Y

ij

ijij 1

(1)

where ]L,L[U~ maxminijη , [.]U denotes the uniform random values and q is the noise ratio.

B. Noise Detection algorithm It is easy to detect salt and pepper noise because the noisy

pixels value will be either 0 or 255. But, in the random valued impulse noise the gray values are from 0 to 255. Hence, it is very difficult to differentiate the noisy pixel from noise free pixel. The noise detection algorithm for random noise is given as:

Step 1: Select the processing pixel, Yij and the neighborhood pixels are denoted by Wst.

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Figure 1. Flow chart of the proposed algorithm

Random Valued Noisy Image

Select 2D 3 x 3 window with center element as P(i,j) as a processing pixel

Find the absolute difference value for P(i,j) with its neighbors

N1 > N2

Find the difference between absolute difference values (D)

YES NO

T1 > T2

-Th1< D(i) < Th1

Retain the corresponding neighbor pixel

YES

YES

Remove the corresponding neighbor pixel

NO

Replace the processing pixel with the median value

-Th1< D(i) < Th1

NO

Retain the corresponding neighbor pixel

YES

NO

Take next or previous difference value

YES

NO

Remove the corresponding neighbor pixel

Current > Next/ Previous

Denoised Image

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Step 2: Find the absolute differences between processing pixel and neighborhood pixels, which is denoted as( D~ )

ijtj,si ywD~ −= ++ (2)

where N is the size of the selected window, s and t is varying from - ⎣ ⎦2

N to ⎣ ⎦2N .

Step 3: Find the number of smallest absolute difference (N1) and the number of largest absolute difference (N2).

Step 4: The processing pixel is noisy or noise free is detected by the value of N1 and N2. The noisy pixel is determined as

⎩⎨⎧ <

=otherwise,

NNifZ j,i 0

1 21 (3)

The ‘1’ represents the noisy pixel and ‘0’ denotes the noise free pixel. The reason is that the tested pixel to be considered as an original should be similar to the pixels with the minimum absolute difference.

C. Noise Reduction Algorithm After detecting the noisy pixel, it should be replaced by

noise free pixels in the neighborhood. The noise reduction algorithm is given as:

Step 1: First check the processing pixel is noisy or noise free using noise detection algorithm. If the processing pixel is noise free, then that processing pixel is unaltered.

Step 2: If the processing pixel is noisy then take 3 x 3 window neighborhood pixels. In the neighborhood, pixels are removed if they are noisy. The noisy pixels in the selected window are obtained by the difference of the first absolute difference. The detailed explanation of this noise estimation is shown in figure 1. The remaining pixels are considered for median value estimation. This median value replaces the noisy processing pixel.

Step 3: Repeat the process for entire image.

The detailed explanation of the proposed algorithm is given in figure 1.

II. ILLUSTRATION OF THE PROPOSED ALGORITHM Each and every pixel of the image is checked for the

presence of impulse noise using absolute difference value. Different cases are illustrated in this section. The noise free condition is illustrated in case (i). Case (ii) deals with the condition that the processing pixel is noisy and its neighbors are noise free. Similarly some of the other cases are discussed in this section. The illustration of the proposed algorithm is shown in figure 2.

Case (i): Let us consider the pixel 154 is a processing pixel, First check the processing pixel is noisy or noise free. Find the absolute difference between the processing pixel and with its neighborhood. The absolute differences are {2, 5, 4, 6, 3, 8, 5, 4}. Here the absolute differences are very less, hence, the processing pixel is noise free, and the processing pixel is unaltered.

Case (ii): In this case 57 is a processing pixel, the absolute difference between 57 and its neighbors are {98, 101, 99, 101, 102, 98, 101, 99}. The absolute differences are higher value; hence the pixel 57 is a noisy pixel. The noisy pixel is removed in the consecutive filtering process (i.e.) find the median value of the sort pixels without 57. So, the median value ({155 155 156 156 158 158 158 159}) is (156+158)/2 = 157. This value replaces the noisy pixel.

Case (iii): In case (iii) 153 is a processing pixel and the absolute value differences are {7, 1, 4, 3, 2, 2, 2, 77}. Here all values are less except 77. Because of the majority of the differences are very less, the processing pixel is considered as noise free and is unaltered.

Case (iv): The pixel 159 is a processing pixel and the absolute differences are {146, 2, 0, 97, 126, 2, 3, 0}. Here, the count of highest difference is 3 (N2), which is less than the count of lowest difference (N1). Hence we consider the processing pixel is noise free and is unaltered.

(a) Original Image (b) Noisy Image

(c) Illustration of Different cases

Figure 2. Illustration of the proposed algorithm

Case (v): In this case 140 is the processing pixel and the absolute differences are {19, 5, 18, 15, 15, 19, 59, 18}.The absolute differences are not lesser value except 5. Hence, the processing element pixel is noisy. In this case the lowest and highest differences are 5 and 59 respectively. The remaining values are within that range {19, 18, 15, 15, 19, 18} and the corresponding pixels are {159, 158, 155, 155, 159, 158}. Because 5 and 59 are the lowest and highest absolute difference it indicates that the corresponding pixels are noisy. So the noisy pixel is replaced by median value of the pixels {159, 158, 155, 155, 159, 158}. In this case we need some other parameter to estimate the noisy pixel, which has the threshold value (T1 and T2). This threshold value is used to determine the neighborhood pixels are either noisy or noise free.

The absolute difference is the measure used to make a decision whether the pixel is noisy or noise free. This method is very simple for low noise density. But, at high noise densities, selecting the threshold is a challenging issue.

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(a) Original Image (b) Noisy Image (c) PSM (d) PWMAD

(e) MSM (f) EPRIN (g) ODRIN (h) Proposed

Figure 3. Results of the different algorithms for Baboon image

(a) Original Image (b) Noisy Image (c) PSM (d) PWMAD

(e) MSM (f) EPRIN (g) ODRIN (h) Proposed

Figure 4. Results of the different algorithms for Bridge image

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TABLE I. COMPARISON FOR BABOON IMAGE IN TERMS OF PSNR IN DB

TABLE II. COMPARISON FOR BRIDGE IMAGE IN TERMS OF PSNR IN DB

III. RESULTS AND DISCUSSION Gray scale images like Baboon and Bridge are used to

analyze the performance of the proposed algorithm with different noise densities. Denoising performances are quantitatively measured by the Peak Signal to Noise Ratio (PSNR) in dB is defined as

⎟⎟⎠

⎞⎜⎜⎝

⎛=

MSElogPSNR

22551010 (1)

where ( )∑∑ −=i j

)j,i(X)j,i(YMN

MSE21 , MSE is an

acronym for mean square error, Y denotes the denoised image, X is the original image and MN represents the size of the original image.

By varying the noise densities from 20 to 90% ,the PSNR values of the proposed algorithm is compared with the existing algorithms for Baboon and Bridge images and their corresponding results are shown in table I and table II respectively. From the tables, it is evident that the proposed algorithm is always better than the existing algorithms at different noise densities.

The reconstructed Baboon and Bridge images using the existing and proposed algorithm are shown in Figure 3 and 4 respectively. Baboon and Bridge images are corrupted with 40% and 60% noise density respectively. From the figures, it is evident that the quality of the image obtained using the proposed algorithm is better than the quality of the image obtained using the existing algorithms.

IV. CONCLUSION In this paper, a new algorithm is proposed for removing

random valued impulse noise. The proposed algorithm is simple and efficient in which the noise detection is based on the absolute difference between the processing pixel and its neighborhood pixels. The noise reduction is through modified median filtering approach. The proposed algorithm gives better results than the existing algorithms both quantitatively and qualitatively.

REFERENCES [1] J. Astola and P. Kousmanen, Fundamentals of Nonlinear Digital

Filtering. CRC Press, 1997. [2] T. Sun and Y. Neuvo, “Detail-preserving median based filters in image

processing,” Pattern Recognit. Lett., vol. 15, pp. 341–347, Apr. 1994. [3] E. Abreu, M. Lightstone, S. K. Mitra, and K. Arakawa, “A new efficient

approach for the removal of impulse noise from highly corrupted images,” IEEE Trans. Image Processing, vol. 5, pp. 1012–1025, June 1996.

[4] D. A. F. Florêncio and R. W. Schafer, “Decision-based median filter using local signal statistics,” Proc. SPIE, vol. 2308, pp. 268–275, Sept. 1994.

[5] F. Russo and G. Ramponi, “A fuzzy filter for images corrupted by impulse noise,” IEEE Signal Processing Lett., vol. 3, pp. 168–170, June 1996.

[6] H. Kong and L. Guan, “A noise-exclusive adaptive filtering framework for removing impulse noise in digital images,” IEEE Trans. Circuits Syst. II, vol. 45, pp. 422–428, Mar. 1998.

[7] T. S. Huang, G. J. Yang, and G. Y. Tang, “Fast two-dimensional median filtering algorithm,” IEEE Transactions on Acoustics, Speech, and Signal Processing, 1 (1979), pp. 13–18.

[8] Z. Wang and D. Zhang, “Progressive switching median filter for the removal of impulse noise from highly corrupted images,” IEEE Trans. Circuits Syst. II, vol. 46, no. 1, pp. 78–80, 1999.

[9] H. Yu, L. Zhao, and H. Wang, “An efficient procedure for removing random—Valued impulse noise in images,” IEEE Signal Process. Lett., vol. 15, no. 1, pp. 922–925, Dec. 22, 2008.

[10] Y. Dong, R. H. Chan, and S. Xu, “A detection statistic for random valued impulse noise,” IEEE Trans. Image Process., vol. 16, no. 4, pp. 1112–1120, April 2007.

[11] W. Luo and D. Dang, “A new directional weighted median filter for removal of random-valued impulse noise,” IEEE Signal Process. Lett., vol. 14, no. 3, pp. 193–196, Mar. 2007.

[12] J.-F. Cai, R. H. Chan, and M. Nikolova, “Fast two-phase image deblurring under impulse noise,” J. Math. Imag. Vis., vol. 36, no. 1, pp. 46–53, 2010.

[13] V. Crnojević, V. Šenk, and Ž. Trpovski, “Advanced impulse detection based on pixel-wise MAD,” IEEE Signal Process. Lett., vol. 11, no. 7, pp. 589–592, Jul. 2004.

[14] A. S. Awad, “Standard Deviation for obtaining the Optimal Direction in the Removal of Impulse noise”, IEEE signal processing Letters, vol. 18, no. 7, July, 2011.

Method PSNR in dB

20% 30% 40% 50% 60% 70% 80% 90%

PSM 22.88 21.73 20.90 20.14 19.15 17.47 15.22 13.55

PWMAD 23.53 20.93 18.65 16.44 14.56 13.16 11.92 10.91

TSM 16.28 16.08 16.18 16.16 16.13 16.22 16.17 16.25

MSM 22.06 20.06 18.10 16.11 14.69 13.86 12.12 12.01

EPRIN 21.47 21.91 21.16 20.61 20.43 19.05 15.85 13.62

ODRIN 21.67 21.36 21.21 20.72 20.79 19.29 16.70 14.05

Proposed 24.21 23.86 23.51 23.25 22.51 22.56 21.96 17.41

Method PSNR in dB

20% 30% 40% 50% 60% 70% 80% 90%

PSM 25.57 23.73 22.21 20.93 19.38 17.86 15.68 13.79

PWMAD 23.78 21.10 18.69 16.99 14.43 13.48 11.31 10.93

TSM 16.68 16.27 16.14 16.17 16.27 16.37 16.83 16.51

MSM 24.84 21.31 18.65 16.57 14.87 13.94 12.99 12.93

EPRIN 24.78 23.32 23.88 22.38 21.16 19.65 17.13 13.88

ODRIN 24.58 23.84 23.74 22.52 21.31 20.96 17.62 14.29

Proposed 26.52 25.54 24.75 24.56 23.54 23.14 22.36 17.85