adaptive filter for gaussian noise
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Volume 1, No. 9, November 2012 ISSN 2278-1080The International Journal of Computer Science &
Applications (TIJCSA)RESEARCH PAPER
Available Online athttp://www.journalofcomputerscience.com/
2012,http://www.journalofcomputerscience.com-TIJCSAAllRightsReserved 9
Adaptive Fuzzy Approach to Gaussian Noise Removal
in Gray Scale Images
Deepinder Kaur1
Department of Computer Science & Engineering,
B.B.S.B.E.C,
Fatehgarh Sahib(Punjab), India
deepinder_kr@yahoo.co.in
Baljit Singh2
Department of Computer Science & Engineering,
B.B.S.B.E.C,
Fatehgarh Sahib(Punjab), India
baljitkhehra@rediffmail.com
Abstract
Visual information transmitted in the form of digital images is becoming a major method of
communication in the modern age, but the image obtained after transmission is often corrupted
with noise. The received image needs processing before it can be used in applications. A New
Fuzzy Filter that adopts Fuzzy Logic is proposed in this paper which removes Gaussian Noise
from the Corrupted Gray scale Images. The main concern of the present filter is to distinguish
between local variations due to noise and due to image structure. It uses 14 fuzzy rule based
convolution mask on every pixel of the image. Objective performance of the proposed algorithm
is compared with conventional methods based on Mean Square Error (MSE), Root Mean Square
Error (RMSE), Signal to Noise Ratio (SNR) and Peak Signal to Noise Ratio(PSNR). The results
illustrate that the proposed method can be used as an effective Noise removal method for
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DeepinderKaur,BaljitSingh,TheInternationalJournalofComputerScience&Applications(TIJCSA)
ISSN2278-1080,Vol.1No.9November2012
2012,http://www.journalofcomputerscience.com-TIJCSAAllRightsReserved 10
Gaussian noise. Results show that by using the proposed method improved SNR and PSNR and
minimized MSE and RMSE are achieved. Hence proposed algorithm leads to better image
enhancement.
Keywords: Fuzzy logic; Gray scale; Median Filter; Mean Filter; Gaussian noise; Impulse
noise; Multiplicative Noise; Correction term.
1. IntroductionDigital images are used in various applications in todays life. Digital images are corrupted by
noise during image acquisition or transmission process. There are different types of noises indigital images. For example, Additive white Gaussian noise (AWGN) is due to image sensors
operating at low light levels, poor image acquisition or by transferring the image data in noisycommunication channels. Gaussian noise is statistical noise that has its probability density
function equal to that of the normal distribution, which is also known as the Gaussiandistribution. In other words, the values that the noise can take on are Gaussian-distributed.
Gaussian noise is properly defined as the noise with a Gaussian amplitude distribution. This saysnothing of the correlation of the noise in time or of the spectral density of the noise. Labeling
Gaussian noise as 'white' describes the correlation of the noise. It is necessary to use the term"white Gaussian noise" to be precise. Gaussian noise is sometimes misunderstood to be white
Gaussian noise, but this is not the case.
Noise is modeled as additive white Gaussian noise (AWGN), where all the image pixelsdeviate from their original values following the Gaussian curve. That is, for each image pixel
with intensity value fij
(1 i m, 1 j n for an m x n image), the corresponding pixel of the
noisy image gij
is given by,
(1)
where, each noise value n is drawn from a zero -mean Gaussian distribution as shown in fig 1.
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DeepinderKaur,BaljitSingh,TheInternationalJournalofComputerScience&Applications(TIJCSA)
ISSN2278-1080,Vol.1No.9November2012
2012,http://www.journalofcomputerscience.com-TIJCSAAllRightsReserved 11
Fig 1. Gaussian Distribution Curve
Denoising is the pre-processing step in the Image Enhancement process. Denoising isnecessary and first step to be taken before the image data is analyzed for further use. Because
after introducing the noise in image, the important details and features of image are destroyed. Itis necessary to apply efficient denoising technique to compensate for such data corruption. Image
denoising is used to remove the noise while retaining as much as possible the important signalfeatures. The purpose of image denoising is to estimate the original image from the noisy data.
2. Existing Methods
Generally, the Gaussian noise can easily be removed by locally averaging the pixels inside thewindow and replace the current pixel with this average value. Conventional linear filters such as
arithmetic mean filter and Gaussian filter smooth noises effectively but blur edges. Statisticalcharacteristics of images are of fundamental importance in removing Gaussian noise. The well
known wiener filter assumes the images are second order stationary. But for most natural imagesthe stationary assumption is not valid. The Wiener filter [2] experiences uniform filtering
throughout the image, with an unacceptable blurring of fine detail across edges and inadequatefiltering of noise in relatively flat areas. To overcome the problem of linear filtering, non-linear
filtering techniques become popular as an alternative to preserve signal structure. Median filter[3][4]is quite popular non linear denoising filter because it provide excellent noise reduction
capabilities with considerably less blurring than linear smoothening filters of same size. Forimpulsive noise, the median filter is one of the best. But for Gaussian noise, it is less successful.
A compromise between the mean and median is trimmed mean filters. The idea behind atrimmed mean is to reject the most probable outliers-some of the very smallest and very largest
values and average the rest. Alpha trimmed mean filter [5] is a one which performs the operationof both mean and median filter based on the value of. It gives better noise reduction with some
smoothening capabilities. The K-nearest neighbour filter [6] also a trimmed mean filter. Ithandles only the values closest to the value of the center sample. The value K decides the
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smoothening capability. In [7] Perona and Malik have proposed an anisotropic diffusion method
for Gaussian noise removal. In [8] Tomasi and Manducci have proposed a bilateral filter toremove Gaussian noise with edge preservation. Recently Tamer Rabie [9] proposed a robust
estimation based algorithm to remove gaussian noise. It effectively removes low to mediumdensity Gaussian noise with edges are better preserved. In [10] R.Garnett and T.Huegerich have
proposed a universal noise removal algorithm to remove Gaussian noise and other types ofnoises. In all these methods complexity of the algorithm is high. In this paper we proposed a
Fuzzy rule based method to remove low to high density Gaussian noise with detailspreservation.
3. Proposed Method
Fuzzy set theory [11,12,13] has been successfully applied to pattern recognition fields. It is
suitable for dealing with problems containing high levels of uncertainty, to which class patternrecognition or image processing problems usually belong. Obviously, the recovery of heavilynoise-corrupted images is a task with high uncertainty levels. The general idea behind the filter is
to average a pixel using other pixel values from its neighborhood, but simultaneously to take careof important image structures such as edges. The main concern of the present filter is to
distinguish between local variations due to noise and due to image structure. It uses 14 fuzzy rulebased convolution mask on every pixel of the image. Fuzzy membership functions used in this
algorithm are not static instead it uses an adaptive approach based on the neighborhood pixels.The 3*3 mask selected for image scanning passes on pixel values to the fuzzy system input. In
this mask each pixel is considered as an input image processing values between 0-255. Valuesof the mask are obtained by hit and trial method. Rules are determined based on pixel vicinity
status. These rules have been written studying different states and special edge conditions. Theconsidered 3*3 mask scans all image gray surfaces and pixels are examined according to
predefined rules[19,20,21].
Algorithm:
Step-1: Take Noisy Image as Input image.
Step2: Repeat the steps 3 to 8 for each pixel present in the input image.
Step3: Consider current pixel as Center Pixel (Centre_pixel).
Steps4: Clear the values Linear arrays Fuzzy[] and Possible_outcomes[].
Step5: Apply 14 Fuzzy rule based filter masks on the Centre_pixel and initialize the linear arrayFuzzy[] by Fourteen different responses Ri.
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X X X
X X
X
X X
X
X
X
X
X XX
X
X X
X
X
X
XX X
X
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Fig 2: The collection of fuzzy masks
Step6. Update Linear array Possible_outcomes[] with the values of linear array Fuzzy[]according to the following rules:
a) Add The values of linear array Fuzzy[] to Possible_outcomes[] if the values lies betweenthe range of Value(Left_pixel) and Value(Centre_pixel). Do not repeat the contents ifalready exists in linear array possible_outcomes[].
b) Add The values of linear array Fuzzy[] to Possible_outcomes[] if the values lies betweenthe range of Value(Right_pixel) and Value(Centre_pixel). Do not repeat the contents if
already exists in linear array possible_outcomes[].c) Add The values of linear array Fuzzy[] to Possible_outcomes[] if the values lies between
the range of Value(Up_pixel) and Value(Centre_pixel). Do not repeat the contents if
already exists in linear array possible_outcomes[].d) Add The values of linear array Fuzzy[] to Possible_outcomes[] if the values lies betweenthe range of Value(Down_pixel) and Value(Centre_pixel). Do not repeat the contents if
already exists in linear array possible_outcomes[].
Step7: Sort the contents of linear array Possible_outcomes[] in ascending order.
Step8: Find the median M from the contents of Linear array Possible_outcomes[] .
Step 9: Set Value[Center_pixel]=M in output image.
Step 10: Exit.
X
X X
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Output Image
Fig 3. Flowchart for proposed algorithm
4. Results And Conclusions
The proposed algorithm has been implemented on a set of different digital images. Fuzzy Logic
has been used to get the denoised image of any digital image. All the simulations are done using
VB.Net.
NOISY IMAGE
APPLY 3*3 CONVOLUTION
MASK IN ALL POSSIBLE WAYS
APPLY FUZZY RULES TO SELECT
THE REQUIRED POSSIBLE
OUTCOMES
FIND MEDIAN OF ALL POSSIBLE
OUTCOMES
KNOWELDGE BASE
CORRECTION
TERM
REPLACE THE CURRENT PIXEL
WITH MEDIAN
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Noisy Image Mean Filter
Median Filter Proposed Algorithm
Fig4. Comparison of Filters for Figure 1.tif with noise variance 2.6
Table 1. Comparison of MSE of existing filters with proposed algorithm for 1.tif
Variance( ) 1 1.4 1.8 2.2 2.6
Mean Filter 0.0077 0.0043 0.0026 0.0020 0.0016
Median Filter 0.0011 0.0005 0.0003 0.0002 0.0002
Proposed
Algorithm
0.0006 0.0002 0.0001 0.0001 0.0001
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Table 2. Comparison of RMSE of existing filters with proposed algorithm for 1.tif
Variance( ) 1 1.4 1.8 2.2 2.6
Mean Filter 0.0880 0.0657 0.0517 0.0448 0.0408
Median Filter 0.0341 0.0238 0.0182 0.0156 0.0142
Proposed
Algorithm
0.0246 0.0170 0.0130 0.0113 0.0103
Table 3. Comparison of SNR of existing filters with proposed algorithm for 1.tif
Variance( ) 1 1.4 1.8 2.2 2.6
Mean Filter 0.5260 0.3483 0.2558 0.2123 0.1863
Median Filter 0.7862 0.5359 0.3984 0.3322 0.2930
Proposed
Algorithm
2.2095 1.6426 1.2675 1.0701 0.9427
Table 4. Comparison of PSNR of existing filters with proposed algorithm for 1.tifVariance( ) 1 1.4 1.8 2.2 2.6
Mean Filter 69.231 71.773 73.854 75.093 75.897
Median Filter 77.456 80.587 82.900 84.227 85.032
Proposed
Algorithm
80.279 83.519 85.801 87.064 87.829
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0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
1 1.4 1.8 2.2 2.6
MSE
VARIANCE
MeanFilter
MedianFilter
FuzzyFiltering
Fig 6. Comparison of MSE of existing filters with proposed algorithm for 1.tif
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
1 1.4 1.8 2.2
RMSE
VARIANCE
MeanFilter
MedianFilter
FuzzyFiltering
Fig 7. Comparison of RMSE of existing filters with proposed algorithm for 1.tif
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0
0.5
1
1.5
2
2.5
1 1.4 1.8 2.2 2.6
SNR
VARIANCE
MeanFilter
MedianFilter
FuzzyFiltering
Fig 8. Comparison of SNR of existing filters with proposed algorithm for 1.tif
0
1020
30
40
50
60
70
80
90
100
1 1.4 1.8 2.2 2.6
PSNR
VARIANCE
MeanFilter
MedianFilter
FuzzyFiltering
Fig 9. Comparison of PSNR of existing filters with proposed algorithm for 1.tif
This thesis has briefly overviewed the methods for Gaussian Noise Removal so many methodshave been proposed till now but the proposed algorithm has shown better results. The work
presented in this thesis concludes that Fuzzy Based Approach is best method for yieldingdenoised images provided appropriate Fuzzy rules are chosen. Improved value of SNR, PSNR
and minimized value of MSE and RMSE of proposed algorithm shows that objectiveperformance improvement is achieved. In the proposed method all the techniques and operations
provide an efficient working and the output image is enhanced according to the usersrequirements. Proposed Filter can clean an image completely of noise without making it blurry.
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2012,http://www.journalofcomputerscience.com-TIJCSAAllRightsReserved 21
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