Adaptive Window Size Median Based Filter for Impulse Noise Removal in Digital Images

Adaptive Window Size Median Based Filter for Impulse Noise Removal in Digital Images

Sureshkumar Natarajan Snigdha Saxena

Department of Electronics & Telecommunication Department of Mathematics Vishwaniketans Institute of Management Pillais Institute of Information Technology Enterprenuership and Engineering Technology New Panvel, Maharashtra, India [iMEET], Khalapur, Panvel, Maharashtra,India

Abstract: In this paper, a new non-linear filter called adaptive window size median based filter for removing salt and pepper noise and random valued impulse noise with edge and detail preservation is presented. In the proposed method, the corrupted pixels are replaced by the median value of the uncorrupted pixels in the filtering window after identifying the impulse pixel based on threshold values. Since the proposed algorithm takes a decision whether the pixel under test is corrupted or not, it works well up to a noise density as high as 70% with much lower computation time compared to the other standard techniques. Experimental results clearly indicate that the proposed method surpasses many of the existing methods such as standard median filter, weighted median filter, centre weighted median filter, recursive weighted median filter, progressive switching median filter and other proposed decision based algorithm in terms of visual quality and quantitative measures.

Keywords: Salt and pepper noise, Random valued noise, Median filter.

1. INTRODUCTION

   Generally, image acquired by camera sensors and image transmission through communication channels adds impulse noise in an image [1]. The intensity of impulse noise has the tendency of being either relatively high or relatively low. Thus, it could severely degrade the image quality and cause some loss of information details to remove impulse noise, image de-noising is very important for further image processing. Impulse noise are classified as random valued impulse noise and fixed value impulse noise. Random valued impulse noise can take any value in the dynamic range of the image. Fixed value impulse noise also called as salt and pepper noise can take either minimum value (i.e.0) or maximum value (i.e.255) in the dynamic range [2].

   In the past, various filtering techniques have been proposed for removing impulse noise. It is well-known that linear filters could produce serious image blurring. As a result, nonlinear filters [1], [2] have been widely exploited due to their much improved filtering performance, in terms of impulse noise attenuation and edge/details preservation The standard median filter replaces every pixel by its median value from its neighborhood and often removes desirable details in the image. Specialized median filters such as weighted median filter[1] and central weighted

   median filter [1] recursive weighted median filter [3] were proposed to improve the performance of the median filter by giving more weight to some selected pixels in the filtering window. But they are still implemented uniformly across the image without considering whether the current pixel is noise free or not.

   Therefore, noise-detection process to discriminate between uncorrupted pixels and the corrupted pixels prior to applying non-linear filtering is highly desirable. Some of the decision based algorithm such as progressive switching median filter [4], median type noise detector [5], and decision based algorithm [6] has been reported in the literature. This algorithm first detects the noisy pixels and removes it by applying either standard median filter or its variants. These filters are effective in removing low to medium density impulse noise. Detail Preserving Median Based filter For Impulse Noise Removal In Digital Images has also been studied [7], but it does not give clear details about the threshold value for the random valued impulse noise. In the present work we have also estimated the execution time taken in case of all filtering window size.

   In this paper, adaptive window size median based filter for impulse noise detection and removal is proposed to remove low to medium density salt and pepper noise and random valued impulse noise with edge and fine detail preservation. The proposed algorithm takes a decision whether the pixel under test is corrupted or not before applying the median filter. In order to improve the noise removal capability of the proposed filter, adaptive window length technique is incorporated in the filtering stage.

   The organization of the paper is as follows: Section 2 gives the noise model used in this paper. The proposed algorithm is described in the section 3, illustration of the algorithm is given in section 4 and results and discussions is described in section 5 and section 6 concludes the paper.

2. NOISE MODEL

   The salt and pepper (SP) noise is also called as fixed- valued impulse noise will take a gray level value either minimal (0) or maximum (255) in the dynamic range [0- 255]. It is generated with equal probability. In case of salt and pepper noise, the image pixels are randomly corrupted by either 0 or 255. Salt and pepper noise is mathematically represented as:

   f (x, y) with probability p 1 d

   1. Separation of uncorrupted pixel and corrupted pixels can

      f (x, y) 0

      p d / 2

      (1)

      be done by using following step,

      SPN

      1

      p d / 2

      X *

      1,

      0,

      ij

      ij

      1

      0

      (6)

      where d is the noise density

3. PROPOSED ALGORITHM

   The proposed algorithm is basically a two stage algorithm, in which the first stage is used to detect impulse noise and second stage is used to replace the corrupted pixels with median value of uncorrupted pixel in the filtering window. This algorithm works both for fixed valued impulse noise and random valued impulse noise.

   Let X denote the noise corrupted image of size MxN

   1. Apply a filtering window of initial size 3×3 to the noisy pixels whose values are zero in the matrix ( X * ) and

      replace the noisy pixel with the median value of the uncorrupted pixel in the window.

   2. If the number of uncorrupted pixels in the window is at least three, otherwise window size is increased to 5×5. Table 1 shows the noise density with corresponding window size.

   Table I. Noise density Vs window size

   Noise Density	Window size
   10% < < 30%	3×3
   40% < < 60%	5×5
   70% < < 90%	7×7

   (i.e.1 i M , 1

   j N ) and for each pixel

   X (i, j)

   denoted as xij , a sliding window of size

   ( (2L 1)x(2L 1) ) centered at

   X ij

   is defined. The

   steps of the algorithm are as

   1. Get the noisy image as X .

   2. Let

      xij

      be the current pixel to be processed; Wij is the

      sliding window of size (2L 1)x(2L 1) centered at xij . The elements of this window

4. ILLUSTRATION OF ALGORITHM

   Wij

   {xi j,uv ,

   • L u, v L}

   (2)

   1. Apply a 3×3 noise detection filtering window to the entire pixels in the image.

   2. Find the absolute difference (AD) between the centre pixel values with the neighboring pixels in the corresponding window as

      A 5×5 image segment from a 10% noise corrupted Lena image is considered.

      Original Image Noisy Image

      Segent Segment(SPN)

      1,

      0 xi j,uv xij T

      31

      63 145

      80 14 6

      31

      63 145

      80 1 46

      i j,uv

      8

      0,

      otherwise

      (3)

      37 81 126

      175

      37 81 126 0 8

      36 31

      61 26

      94 36 31 61 26

      255

   3. Count the number of pixels whose absolute difference

      lies in between zero to particular threshold

      34 22

      76 11

      84 34 22 76 0

      84

      ( 0 AD T ). For optimum performance the threshold value ( T ) chosen to be 40 for salt & pepper noise (SPN)

      5

      110

      80 192

      169

      5

      110

      80 192

      169

      and 10 for random valued impulse noise (RVIN).

      Applying 3 X 3 Noise Detection Filtering Window on

      ij

      i j,uv

      Lu,vL

      (4)

      Noisy Image Segment.

      where ij

      denotes the number of pixels which are similar

      to that of center pixels.

   4. Let us assume ij

   as same size of the filtering window

   and assigned to one when

   T2 . .

   ij

   is greater than a threshold

   ij

   1,

   ij

   T2

   (5)

   Absolute difference between center pixel and surrounding

   0, otherwise

   pixels are AD = {61, 26, 255, 76, 84,80,192,169}. Hence,

   where T2 is a predefined threshold is chosen to be 2 for

   i j,uv {0,1, 0, 0, 0, 0, 0, 0} . Therefore,

   optimum performance.

   ij 1

   indicates a noise free

   ij

   1 and

   ij

   is set to zero because count is lesser

   pixel. than the threshold value 2. Then multiply the noisy image

   segment with

   ij

   which is shown below. In this example,

   the center pixel is corrupted, hence center pixel is replaced by median value of uncorrupted pixel in the filtering window (i.e. 61, 26, 76). Here the center is replaced by the median value 61. If the center pixel is uncorrupted then that center pixel is retained.

5. RESULTS AND DISCUSSION

   In this section, the proposed algorithm is tested for four different test images such as Lena, Mandrill, bridge and pepper of size 512×512, 8 bits/pixel. All these images are corrupted with different noise densities and applied to the proposed filter. The performance of the proposed filter is compared with the existing filters such as standard median filter (SMF), center weighted median filter (CWMF), weighted median filter (WMF), and recursive weighted median filter (RWMF), Progressive Switching median filter (PSMF) and Decision Based Algorithm (DBA). A quantitative comparison is performed between the various filters and the proposed filter on the basis of four objective quality measures such as peak signal to noise ratio, mean absolute error, structural similarity index and universal quality index as defined as

   2552

   PSNR 10 log10 MSE

   (7)

   MAE

   M

   x1

   N

   y1

   f(x, y) f (x, y) MxN

   (8)

   Fig.1 (a) Original Lena image(b) Noisy image (SPN=60%). Restoration results of (c) SMF (d) WMF (e) CWMF (f) RWMF (g) PSMF (h) DBA (i) Proposed Algorithm

   SSIM (x, y)

   (2x y C1 )(2 xy C2 )

   ( 2 2 C )( 2 2 C )

   (9)

   x y 1 x y 2

   where

   f(x, y)

   and

   f (x, y)

   denote the pixel values

   of the restored image and the original image, respectively.

   MxN is the size of the image. x

   and

   y represent

   the mean of the original and restored images.

   x and

   • y represent the standard deviation of the original and

     restored images.

   • xy

   represent the standard deviation of

   the original and restored image. C1

   and C2

   are small

   constant which and are added to avoid instability [8].

   Fig.2(a) Noisy image (RVIN=40%). Restoration results of (b) SMF (c) WMF (d) CWMF (e) RWMF (f) PSMF (g) DBA (h) Proposed Algorithm

   New Approach (M=1296) (inside training)	36.02 dB	34.44 dB	32.95 dB	31.77 dB	30.49 dB
   New Approach (M=1296) (outside training)	36.64 dB	34.72 dB	32.95 dB	31.52 dB	29.99 dB
   Proposed Algorithm	41.38 dB	40.45 dB	39.74 dB	39.05 dB	38.05 dB

   Table II. Comparative restoration results in PSNR for various percentage of random-valued impulse noise of Lena image.

   Algorithm	Percentage of Random-Valued Impulse Noise
   	10%	15%	20%	25%	30%
   Median Filter(3×3)	32.14 dB	31.01 dB	29.76 dB	28.01 dB	26.20 dB
   New Approach (M=2) no training	35.18 dB	33.94 dB	32.47 dB	31.18 dB	29.87 dB

   Table III. Comparative restoration results in PSNR of various filters for pepper image corrupted by salt and pepper noise at different noise densities

   Table IV. MAE of various filters for pepper image corrupted by salt and pepper noise at different noise densities

   Table V. Comparative restoration results in SSIM of various filters for Lena image corrupted by salt and pepper noise at different noise densities

   Algorithms	SSIM
   SMF( 3 X 3 window size)	0.04868
   WMF( 5 X 5 window size)	0.20708
   CWMF( 5 X 5 window size)	0.09442
   RWMF(2 iteration)	0.3398
   PSMF	0.7113
   DBA	0.6875
   Proposed Algorithm	0.9

   Table VI. Variation of Execution Time (seconds) for various images with respect to noise density for random- valued impulse noise

6. IMPLEMENTATION

   Adaptive window size median based filter for impulse noise removal in digital images is presented to remove salt and pepper noise and random-valued impulse noise with edge and fine detail preservation. The proposed algorithm is implemented in MATLAB 7.0 equipped in a Pentium IV PC. The proposed algorithm is tested with 4 different images such as Lena, Mandrill, Pepper and Bridge,

7. CONCLUSION

The visual quality clearly indicates that it performs much better than other existing filters. The restoration results in terms of PSNR and MAE also confirm better performance of the filter as compare to other existing filters. PSNR of Lena image corrupted with random-valued impulse noise with noise density in the range of 10% to 30% have been calculated. Execution time for various images has also been calculated and it has been observed that the algorithm proposed in the present paper takes less execution time as compared to other existing work.

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