1. Image De-Noising for Salt and Pepper Noise by
Robust Mean Filter
Pranay Yadav1
and Vivek Kumar2
1
TIT, RGPV, Department of ECE, Bhopal, India
Email: pranaymedc@gmail.com
2
LGOI, RGPV, Department of ECE, Bhopal, India
Email: kunwarv4@gmail.com
Abstract—When an image is formed, factors such as lighting (spectra, source, and intensity)
and camera characteristics (sensor response, lenses) affect the appearance of the image.
Therefore, the prime factor that reduces the quality of the image is noise. It hides the
important details and information’s of images. In order to enhance the qualities of image,
the removal of noises become imperative and that should not at the cost of any loss of image
information. Noise removal is one of the pre-processing stages of image processing. In this
paper a new method for the enhancement of gray scale images is introduced, when images
are corrupted by fixed valued impulse noise (salt and pepper noise). The proposed
methodology ensures a better output for low and medium density of fixed value impulse
noise as compare to the other famous filters like Standard Median Filter (SMF), Decision
Based Median Filter (DBMF) and Modified Decision Based Median Filter (MDBMF) etc.
The main objective of the proposed method was to improve peak signal to noise ratio
(PSNR), visual perception and reduction in blurring of image. The proposed algorithm
replaced the noisy pixel by trimmed mean value. When previous pixel values, 0’s and 255’s
are present in the particular window and all the pixel values are 0’s and 255’s then the
remaining noisy pixels are replaced by mean value. The gray-scale image of mandrill and
Lena were tested via proposed method. The experimental result shows better peak signal to
noise ratio (PSNR), mean square error (MSE) and mean absolute error (MAE) values with
better visual and human perception.
Index Terms— blurring, human and visual perception, modified nonlinear filter, salt and
pepper noise, mean square error, peak signal to noise ratio.
I. INTRODUCTION
In the field of image processing, digital images very often get corrupted by several kinds of noise during the
process of image acquisition. The basic reasons are malfunctioning of pixels in camera sensors, faulty
memory locations in hardware, or transmission in a noisy channel [1]. In addition, these are also the main
reasons responsible for generation of the impulse noise in digital world. In the field of image processing,
digital images are mainly corrupted by the impulse noise [2]. There are two types of impulse noise, namely,
the salt-and-pepper noise also known as the fixed valued impulse noise and the random-valued impulse noise
[3], [8]. Impulse noise is one the most severe noise which usually affects the images. Researchers are
© Elsevier, 2013
Proc. of Int. Conf. on Advances in Electrical & Electronics, AETAEE

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involved in the field of image de-noising in order to find out effective method, capable of preserving the
image details, reducing the noise of digital images and ensuring the quality of the image. Image quality
measurement is analyzed by image parameters like peak to single noise ratio (PSNR), mean square error
(MSE), image enhancement factor (IEF)[13], but in case of image processing one more thing of utmost
importance is human perception [4], [9]. In this paper focus is kept upon salt and pepper noise. The salt and
pepper noise corrupted pixels of image take either maximum or minimum pixel value Salt and pepper noise.
Fixed valued impulse noise is producing two gray level values 0 and 255. Random valued impulse noise will
produce impulses whose gray level value lies within a predetermined range. The random value impulse noise
is between 0 and 255. Generally the spatial domain filters have a detection stage which identifies the noisy
and noise free pixels of the corrupted image, after that noise removal part removes the noise from the
corrupted image under process while preserving the other important detail of image [5]. Initially standard
median filter was popularly used, but later on switching based median filters came into existence which
provides better results. Any other result oriented standard median filters are, weighted median filter, SD-
ROM filter, centre weighted median filter, adaptive median filter, rank order median filter and many other
improved filters. The performance of median filters also depends on the size of window of the filter. Larger
window has the great noise suppression capability, but image details (edges, corners, fine lines) preservation
is limited, while a smaller window preserves the details, but it will cause the reduction in noise suppression.
Noise detection is a vital part of a filter, so it is necessary to detect whether the pixel is noise or noise free.
However, further reduction in computational complexity is enviable.
II. LITERATURE SURVEY AND RELATED WORK
A. Mean filter (M.F)
In the 1998 Scott E Umbaugh, Computer Vision and Image Processing, Prentice Hall PTR, New Jersey, A
mean filter acts on an image by smoothing it; that is, it reduces the intensity variation between adjacent
pixels. The mean filter is nothing but a simple sliding window spatial filter that replaces the center value in
the window with the average of all the neighboring pixel values including it. By doing this, it replaces pixels
that are unrepresentative of their surroundings. It is implemented with a convolution mask, which provides a
result that is a weighted sum of the values of a pixel and its neighbors. It is also called a linear filter. The
mask or kernel is a square. Often a 3× 3 square kernel is used. If the coefficients of the mask sum up to one,
then the average brightness of the image is not changed. If the coefficients sum to zero, the average
brightness is lost, and it returns a dark image. The mean or average filter works on the shift-multiply-sum
principle [12].
B. Adaptive median filter (AMF)
In 2008, S.Saudia, Justin Varghese, Krishnan Nallaperumal, Santhosh.P.Mathew, Angelin J Robin,
S.Kavitha, Proposes a new adaptive 2D spatial filter operator for the restoration of salt & pepper impulse
corrupted digital images name as -“Salt & Pepper Impulse Detection and Median based Regularization using
Adaptive Median Filter”, The Adaptive Impulse Filter effectively identifies the impulsive positions with a
valid impulse noise detector and replaces them by a reliable signal determined from an appropriate
neighbourhood. Experimental results in terms of objective metrics and visual analysis show that the proposed
algorithm performs better than many of the prominent median filtering techniques reported in terms of
retaining the fidelity of even highly impulse corrupted images. High objectiveness and visual reliability is
provided by the new restoration algorithm at lower quantum of impulse noise also. The Adaptive Median
Filter (AMF) for salt & pepper impulse noise removal that can give much acceptable and recognizable image
restoration with better visual quality at all impulse noise levels than most other median filters which develop
impulse patches in the output at higher impulse noise levels. Images restored by the proposed filter for Noise
ratio at 95% restoration of the Proposed Filter with better objective metrics and fidelity at higher noise ratios
is an improvement in the field of impulse restoration. The computational efficiency of the proposed filter is
also significant at all impulse noise ratios.
In 2009, Cheng Huang, Youlian Zhu, enhance the previous morphological filter and presented a “New
Morphological Filtering Algorithm for Image Noise Reduction”. Conventional morphological filter is
disabling to effectively preserve image details while removing noises from an image. This algorithm of the
self-adaptive median morphological filter is implemented as follows. First, the extreme value operation is
displaced by the median operation in erosion and dilation. Then, the structuring element unit (SEU) is built
based on the zero square matrix. Finally, the peak signal to noise ratio (PSNR) is used as the estimation
function to select the size of the structuring element. Both the characteristics of morphological operations and

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the SEU determine the image processing effect. Following the increase of the noise density, the conventional
morphological filtering algorithm and the median filtering algorithm become unavailable quickly. However,
the proposed morphological filtering algorithm still has better effect in image noise reduction, especially in
low SNR situations. Thus, the proposed algorithm is obviously superior to others [7].
C. Decision based algorithm (DBA)
In 2009, S. Balasubramanian, S. Kalishwaran, R. Muthuraj, D. Ebenezer, V. Jayaraj presented “An Efficient
Non-linear Cascade Filtering Algorithm for Removal of High Density Salt and Pepper Noise in Image and
Video sequence”, in which an efficient non-linear cascade filter for the removal of high density salt and
pepper noise in image and video is proposed. The proposed method consists of two stages to enhance the
filtering. The first stage is the Decision based Median Filter (DMF), which is used to identify pixels likely to
be contaminated by salt and pepper noise and replaces them by the median value. The second stage is the
Unsymmetrical Trimmed Filter, either Mean Filter (UTMF) or Midpoint Filter (UTMP) which is used to trim
the noisy pixels in an unsymmetrical manner and processes with the remaining pixels The basic idea is that,
though the level of de-noising in the first stage is lesser at high noise densities, the second stage helps to
increase the noise suppression. Hence, the proposed cascaded filter, as a whole is very suitable for low,
medium as well as high noise densities even above 90%. The existing non-linear filters such as Standard
Median Filter (SMF), Adaptive Median Filter (AMF), Weighted Median Filter (WMF), Recursive Weighted
Median Filter (RWMF) performs well only for low and medium noise densities. The recently proposed
Decision Based Algorithm (DBA) shows better results up to 70% noise density and at high noise densities,
the restored image quality is poor. The proposed algorithm shows better image and video quality in terms of
visual appearance and quantitative measures.
D. Modified dision based algorithm (MDBA)
In 2009 an improved version of DBA is used to avoid streaks in images that usually occur in DBA due to
repeated replacement of the noisy pixel with neighborhood pixels. In case of MDBA noisy pixels are
replaced by the median of asymmetric trimmed output. Drawback of MDBA is that under high noise
densities the pixels could be all 0’s or all 255’s or a combination of both 0 and 255. Replacement with
trimmed median value is not possible then.
E. Decision based unsymmetrical trimmed mean filter (DBUTMF)
In 2010 K. Aiswarya, V. Jayaraj, and D. Ebenezer, proposed a new method for removal of high density salt
and pepper noise (SNP) that is – “A new and efficient algorithm for the removal of high density salt and
pepper noise in images and videos,” in Second Int. Conf. Computer Modeling and Simulation. To overcome
the above drawback, Decision Based Algorithm (DBA) is proposed. In this, image is denoised by using a 3x3
window. If the processing pixel value is 0 or 255 it is processed or else it is left unchanged. At high noise
density the median value will be 0 or 255 which is noisy. In such case, neighboring pixel is used for
replacement. This repeated replacement of neighboring pixel produces streaking effect. In order to avoid this
drawback, Decision Based Unsymmetric Trimmed Median Filter (DBUTMF) is proposed [11],[10].
F. Modified decision based unsymmetrical trimmed mean filter (MDBUTMF)
In 2011 S. Esakkirajan, T. Veerakumar, Adabala N. Subramanyam, and C. H. Prem Chand proposed a new
method forremoval of high density salt and pepper noise (SNP) that is –“Removal of High Density Salt and
Pepper Noise through Modified Decision Based Unsymmetric Trimmed Median Filter”. Modified Decision
Based Unsymmetric Trimmed Median Filter (MDBUTMF) is a non linear filter that can perform better in
SAP noise removal even under high noise densities. MDBUTMF is used for the noise detection and removal
process in this thesis. The filtering process consists of initially detecting noisy pixels. Each and every pixel of
the image is checked for the presence of salt and pepper noise. The processing pixel is checked whether it is
noisy or noise free. That is, if the processing pixel lies between maximum and minimum gray level values
(between 0 and 255) then it is noise free pixel, it is left unchanged. If the processing pixel takes the maximum
or minimum gray level (0 or 255) then it is noisy pixel which is processed by MDBUTMF [2].
G. Modified Non-linear filter (MNLF)
In 2013 T.Sunilkumar, A. Srinivas, M. Eswar Reddy and Dr. G. Ramachandra Reddy proposed a new method
yields better results at very high noise density that is at 80% and 90% and gives better Peak Signal-to-Noise
Ratio (PSNR).The logic behind this paper that is Alpha Trimmed Mean Filtering (ATMF) is ̠ symmetrical
filter. As symmetric at either end even un-corrupted pixels are trimmed. This leads to loss of image details
and blurring of the image. In order to overcome this drawback, an Un-symmetric Trimmed Median and Mean

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Filter are found. In this method, the selected 3 x 3 window elements which contain 0’s or 255’s or both are
removed. Then the median or mean value of remaining pixels is taken. This median or mean value is replaced
in corrupted pixel value [13].
III. NOISE MODAL
Two common types of the impulse noise are the Fixed-Valued Impulse Noise (FVIN), also known as Salt
and-Pepper Noise (SPN), and the Random-Valued Impulse Noise (RVIN). They differ in the possible values
which noisy pixels can take [6]. The FVIN is commonly modeled by
)1....(..........
,
1)255,0(
)(










pprobabiltywith
ji
X
pprobabiltywithij
Y
Where x(i,j) and y(i,j) denote the intensity value of the original and corrupted images at coordinate (i,j),
respectively and p is the noise density. This model implies that the pixels are randomly corrupted by two
fixed extreme values, 0 and 255 (for 8-bit grey-scale images), with the same probability.
A model is considered as below:
)2..(..........
1
,
1),0(
2)255,255(
)(

















pprobabiltywith
ji
X
pprobabiltywithm
pprobabiltywithmij
Y
Where p = p1 + p2. We refer to this model as Random valued Impulse Noise (RVIN).
IV. PROPOSED METHODOLOGY
The proposed method deploys the enhancement by Modified Non-linear Filter (MNF) [13] algorithm. In this
method first task is to detect the noisy pixels in the corrupted image. For detection of noisy pixels verifying
the condition whether targeted pixel lies. If pixels are between maximum [255] and minimum [0] gray level
values, then it is a noise free pixel, else pixel is said to be corrupted or noisy. Now we have processed only
with the corrupted pixels to restore with noise free pixels. Further un-corrupted pixels are left unaffected. In
the next steps we use Proposed Robust Mean filter (RMF) which is elucidated as follows.
A. Algorithm
Step 1: Initially in the very first step an image was taken and fixed valued impulses noise (Salt and Pepper
noise) was applied on the image.
Step 2: In the second it had been checked whether the pixels falls in between 0 to 255 ranges or not,
consequently two cases were arises.
X (i,j) = 0<Y (i,j)<255 condition true follow Case-1,
X (i,j) ≠ 0<Y(i,j)<255 condition true follow Case-2.
Where O (i,j) is the image size and Y (i,j) all image targeted pixels.
Case 1- If pixels are between 0< Y (i,j)<255 then, they are noise free and move to restoration image.
Case 2- If the pixels are not lying in between the specified range it is moved towards step 3.
Step 3: In the third step work is done on noisy pixel of step-2. A window of size 3 x 3 of image was selected.
Assuming that the target noisy pixels were W (i,j) and was processed in the next step.
Step 4: If the preferred window does not contains all elements as 0’s and 255’s then remove all the 0’s and
255’s from the window, and send to restoration image.Now find the mean of the remaining pixels was found.
W (i,j) was replaced with the mean value. This removed noise of image was restored as de-noised image at
the last step.
Y (i,j) = [00] condition true send to O (i,j) for Restoration
Y(i,j) = [255] condition true send to O(i,j) for Restoration
[Cal. Mean remain (Y (i,j)) pixels] = replaced by O (i,j)
Step 5: Steps one to three were repeated until all pixels in the whole image was processed. Hence a better de-
noised image was obtained with improved PSNR, MSE and also shows a better image with very low blurring
and improved visual and human perception.
The proposed algorithm based flowchart is shown in Fig. 1. In the flowchart all the conditions have been
mentioned with utmost clarity.

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Figure 1.Flow-Chart diagram of Robust Mean Filter
V. RESULTS
The result of the proposed method for removal of fixed valued impulse noise is shown in this section. For
simulation of proposed algorithm MATLAB 8.0 software is used. The new approach is implemented upon a
‘Real Time Image’ and on ‘Lena’ image size 256X256 as reference images for test conditions. All the test
images taken are gray scale image. The test images are artificially corrupted by Salt and Pepper impulse
noise of different noise density varying from 10% to 90 % on MATLAB. De-noising performances are
quantitatively measured by the PSNR MSE and MAE as defined in equations (3), (4) and (5) respectively:
The PSNR and MSE (Mean Square Error) cab be expressed as:
MSE
(255)
10
2
10logPSNR ... (3)
YES
Read Noise Image (Y)
Select a 3x3 Window with
target Pixel Y (i,j)
If selected
contain all 0 or
255 or both
YESNo
Find Mean of the
Remaining elements
Replace processing pixel
with Mean
Eliminate the elements
with 0 and 255 in the
Window
No
0<Y (i,j)<2555 O (i,j)=Y(i,j)
O (i,j)=Y(i,j)
O(i,j)=Y(i,j)
Replace Processing
Pixels with MEAN

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nm
m
i
n
j
jiYjiY
MSE







1 1
2)},(
^
),({
... (4)
nm
m
i
n
j
jiYjiY
MAE







1 1
),(),(
^
. ... (5)
TABLE I. COMPARISON OF PSNR VALUE OF PROPOSED METHOD WITH EXISTING FILTERS FOR LENA IMAGE
Noise
Density % MF AMF PSMF DBA MDBA MDBUTMF MNLF
New
Approach
10 28.4938 21.9845 30.6494 36.7565 36.7569 38.129 37.3489 38.70
20 25.7542 21.9297 28.2089 33.2606 33.2607 34.6005 34.2358 35.56
30 21.8465 21.4735 25.559 30.5659 30.5308 32.1427 32.1412 33.27
40 18.4076 21.4735 22.6909 28.2609 28.2981 32.0886 30.5796 31.66
50 14.734 20.6542 19.4425 26.2846 26.2503 28.2175 29.0056 30.06
60 12.2348 18.4092 12.8511 24.5361 24.6321 26.5937 27.824 28.56
70 9.9837 14.8564 10.5206 22.7798 22.9338 24.3859 26.0541 26.88
80 8.0229 11.2968 8.4849 20.1441 20.4098 22.0101 24.3291 24.85
90 6.5759 8.0603 6.7847 17.1205 17.2242 17.9865 21.325 21.56
TABLE II. VALUES OF PSNR, MSE AND MAE FOR VARYING NOISE DENSITY OF REAL TIME IMAGE
The PSNR value of the proposed algorithm is compared with other existing algorithms by variable noise
density of 10% to 90%. Table I shows the comparison of PSNR values of different de-noising methods for
Lena image[6][7][8][9][10][12][13]. The PSNR, MSE and MAE of the values proposed new approach for
test images are shown in Table II and Table III. The proposed method not only show better result in terms of
PSNR, MAE and MSE, but also show a good result in visual and human perception and is shown in the
visual quality of the image. Graphical plot of PSNR values of different filters against variable noise densities
for Lena image is shown in Fig. 2. At the end of the manuscript experimental outcomes of the proposed
algorithm for the two test images are illustrated in Fig. 3 and 4.
Noise percentage (%) PSNR MSE MAE Elapsed time (in seconds)
10 33.2335 30.8835 0.9477 3.55
20 31.5689 46.1153 1.4022 3.63
30 30.0751 63.8511 1.8967 3.89
40 28.3339 95.3184 2.5401 4.05
50 27.5656 114.741 3.1323 4.39
60 26.0005 163.174 4.0234 4.85
70 24.1671 249.106 5.4604 5.23
80 22.0612 404.413 7.6634 5.55
90 18.9123 843.459 12.7759 5.99

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TABLE III. VALUES OF PSNR, MSE AND MAE FOR VARYING NOISE DENSITY OF LENA IMAGE
Figure 2. PSNR (dB) Vs Noise Density (%) for Lena image

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Figure 3. Experimental results of proposed method for Lena image with noise density being varied from 10 % to 90 %.
Figure 4. Experimental results of proposed method for real time image with noise density being varied from 10 % to 80 %
The result show better retrieval of images from noise with edge of the images also preserved. Figure 4 shows a real time image de-
noising, here we can see the result of run time image.
Original Image 70% Noise Density Restored Image 80% Noise Density Restored Image
Original Image 50% Noise Density Restored Image 60% Noise Density Restored Image
Original Image 30% Noise Density Restored Image 40% Noise Density Restored Image
Original Image 10% Noise Density Restored Image 20% Noise Density Restored Image
Original Image 90% Noise Density Restored Image
Original Image 70% Noise Density Restored Image 80% Noise Density Restored Image

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VI. CONCLUSION
The performance of the proposed algorithm has been tested at low, medium and high noise densities on gray
scale images and also tested in real time images. Results reveal that the proposed filter exhibits better
performance in comparison with MF, AMF, DBA, MDBA, MDBUTMF, MNF filters in terms of higher
PSNR. Indifference to AMF and other existing algorithms, the new algorithm uses a small 3x3 window
having only eight neighbors of the corrupted pixel that have higher connection; this provides more edge
information, more important to better edge preservation as well as more better Human & visual perception.
Infect at high noise density levels the new proposed algorithm gives better performance as compare with
other existing de-noising filters. In the field of image processing we have not only improved the PSNR, MSE
and MAE as well also require improving the visual quality for both types of images standard image and real
time images. In future we will work on gray scale as well as a color image processing, color image de-
noising and also on 3-D images. Our proposed method takes a very short little time between 2 to 5 second in
10 to 90% noise density, that's why our proposed method is good for field program gate array (FPGA)
simulation. Time consumption shows that the complexity level of our proposed method is very low.
ACKNOWLEDGMENT
The authors wish to thank Mr. Amit Singh (Graduated from Nanyang Technological University, Singapore),
Dr. Abhishek Rawat (Assistant Prof. Samrat Ashok Technical Institute, Vidisha, India) and Mr. Krishna
Kumar Singh (Reserach student of The Robotics Institute, CMU, U.S.A). We are thankful for their valuable
suggestion and timely help.
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