International Journal of Engineering Trends and Technology (IJETT) – Volume 24 Number 2- June 2015
Comparative Analysis of Image De-noising with Different
Filters in Wavelet Domain
Mr.Ashutosh Dwivedi1, Mr.Pratik Soni2, Mr.Virendra k Verma3
Department of Electronics and Communication Engineering, SIMS Indore MP
Abstract- Graphical images are very fundamental type of
data for transmission. Due to the different components
and high speed transmission, image is corrupted by the
noises. Image detection is required during data receiving
end for the faithful communication. There are various
methods for picture denoising in spatial and transform
domain. The present trends of the picture detection
research are the evolution of mixed domain methods. In
this comparison paper, a comparative analysis of picture
denoising using different filters with mixed domain
image denoising method is proposed, which is based on
the wavelet transform, median filter and nonlinear
diffusion based methods. The wavelet transform is used
in this paper to convert the spatial domain image to
wavelet
domain
coefficients.
WT
produces
approximation, horizontal detail, vertical detail and
diagonal detail coefficient which represent the various
spatial frequency bands. The detail component are
removed due to the most of the image part is in
approximation part. Median and wiener filter are used to
apply the filtering on probabilistic way. The trapezoidal
membership function are used for the filtering .The peak
signal to noise ratio (PSNR) and mean square error
(MSE) are used as the performance parameter. The Haar
wavelet is used with various filters to optimize the
performance of denoising.
Keywords: MSE, PSNR, Wavelet Transform.
1.
2. DENOISING METHODS
2.1. Wavelet Transform
The wavelet expansion set is not unique. A wavelet
system is a set of building blocks to construct or
represent a signal or function. While concerning 2D image wavelet decomposition the transform can
be carried out with a vertical operation to obtain
finally four sub image representation [5]. As shown
in figure1 two sub images are generate after 2D
image decomposition original image into two parts
one high frequency coefficient and low frequency.
The image HL is the vertical direction high
frequency component, LH the horizontal direction
high frequency component and LL sub image is the
horizontal and vertical direction low frequency
component and the HH sub image is the diagonal
direction high frequency component. [6].
2.2. Wiener Filter
INTRODUCTION
Denoising picture is a method to make an image
comprehensible to the human visual system. Digital
image are often effect by noise or blurred. Every
digital camera imperfection called noise that is
nothing but noise which affects the image such as
in visual quality and others. Noise may be
classified as substitutive noise (impulsive noise:
e.g., salt and pepper noise, random valued impulse
noise, etc.)[1], additive noise (e.g., additive white
Gaussian noise) and multiplicative noise (e.g.
speckle noise). Types of image denoising are
spatial domain methods and wavelet domain
methods [2]. The special filtering is one of the
classical linear filtering in spatial domain while the
wavelet domain is a new signal estimation method
[3]. Wiener Filter for image restoration of blurred
image, Wiener Filter shows noise as random
process and find estimate of the uncorrupted image
such as mean square error between them in
minimized e.g. wiener filter can be regarded as a
linear estimating method[4]. when we apply
Wavelet transform on 2D image and work with
their detail and approximate coefficient in wavelet
domain ,the wavelet domain is used for
ISSN: 2231-5381
disintegration of image, but still there is some draw
backs for those we will use Fuzzy logic in future
which will be based on triangular member function
(e.g. ATMAV, ATMED FILTERS[10]) and
performance evaluated on MATLAB.
The most important technique for removal of blur
in images due to linear motion or unfocussed optics
is the Wiener Filter. From a signal processing
standpoint, blurring due to linear motion in a
photograph is the result of poor sampling. Each
pixel in a digital representation of the photograph
should represent the intensity of a single stationary
point in front of the camera. Unfortunately, if the
shutter speed is too slow and the camera is in
motion, a given pixel will be an amalgam of
intensities from points along the line of the
camera's motion [7].
The process of extracting the information carrying
signal X(n) from the observed signal Y(n).
Y(n) = X(n) + N(n)
Where: N (n) = noise process
X(n)
X
Y(n)
H(n)
Y(n)
N(n)
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International Journal of Engineering Trends and Technology (IJETT) – Volume 24 Number 2- June 2015
2.3. Median Filter
The Median Filter in the Fourier domain is given
by the expression [8]
median filter is presented to provide optimum
detail preservation along with very high density
noise removal. The quantitative measures in terms
of MSE and PSNR and as well as visual
comparisons, it is evident that for high-density
noise levels Mr. Madeena sultana proposed
algorithm confirms it effectiveness in removing
high-density impulse noises as well as preserving
fine details.
Where:
H (u,v) is the degraded function
H* (u; v) is the complex conjugate of H (u,v)
jH(u; v)j2 = H*(u; v)H(u; v)
S´(u; v) = jN(u; v)j2 is the power spectrum of the
noise
Sf (u; v) = jF (u; v)j2 is the power spectral density
(PSD) of the undergirded image
The above expression is based on the following
assumptions:
Figure 2. Comparison of PSNRs for the
restored “mandrill” image obtained after
applying different filters at different noise
densities. [12]
1. The noise and the image are uncorrelated
2. The noise or the image has zero mean
3. The gray levels in the estimate are a linear
function of the levels in the degraded image.
The Median Filter handles the situation in which
the degradation function is zero, unless both the
degradation function as well as the noise power
spectrum is zero.
3. LITERATURE REVIEW
One of the fundamental challenges is to estimate
the original image by suppressing noise from a
noise-contaminated version of the image. Image
noise may be caused by different intrinsic (i.e.,
sensor) and extrinsic (i.e., environment) conditions
which are often not possible to avoid in practical
situations. Now here there are some problems
which are investigated during the study of papers
on previous years work done
3.1 High Density impulse denoising by A novel
Adaptive Fuzzy Filter by Mr. Madeena Sultana
[12]
Traditional median filters perform well in restoring
the images corrupted by low density impulse noise,
but fail to restore highly corrupted images.
Conversely, the advanced adaptive median filters
are capable of denoising high density impulse noise
but the image details are compromised
significantly. In this paper, a new adaptive fuzzy
ISSN: 2231-5381
The problem in the above methodology is that it
does not minimize the quantization Error as well as
peak signal to noise ratio has not sufficient values
as compare to original value.
3.2 High Performance Filter Based on Statistic
methods for image processing by Pao-ta yu [11]
Experimental results demonstrate that the HPFSM
system achieves high performance for image
processing and outperforms the existing wellknown methods, even if there are many blocks of
noisy pixels at the high noise rate of images
Figure. 3 Comparison of various filters in terms of PSNR
for corrupted “Lena” image. [11]
Simulation results show that the HPFSM system
definitely serves as a perfect image processor and
outperforms the existing well-known filters, even
in many blocks of noisy pixels at the high noise
rate of images.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 24 Number 2- June 2015
This paper has proposed an image processing
technology, called the HPFSM system, which
integrates with Chebyshev’s theorem and a fuzzy
mean process to estimate the Dependable Interval
for impulse noise detection. And a novel method by
the scope of mean-closure function with a Growing
Window is proposed to use for restoring corrupted
pixels.
Now the problem in this research work is still not
improve the peak signal to noise ratio apart from
minimizing the root mean square error.
3.3 Performance Evaluation and comparison of
modified Denoising method and the local adaptive
wavelet image denoising method by Ms. Jignasa M.
permar [10]
The denoising of image is initial step in image
processing. The quality of the denoise image
depends on the two major parts: wavelet transform
for decomposition of image and adaptive wiener
filtering in wavelet domain and spatial domain. The
performance of the local adaptive wavelet image
denoising method is good compared to modified
denoising method in terms of PSNR between
denoise image and original image.
Table: 1 Comparison of both method with PSNR between
original and denoise image at different noise variance
level. [10]
Noise
Variance
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Noise
image
PSNR in db
Modified
denoising
methods
13.8489
11.5180
10.3545
9.6045
9.1220
8.7022
8.3902
8.1842
22.4287
20.7711
19.6614
18.8588
18.2660
17.7009
17.2069
16.9228
The local
adaptive
wavelet
image
denoising
methods
23.4628
21.2357
19.8178
18.9278
18.3018
17.7499
17.2419
17.0181
Hence, from these results it can be concluded that
the local adaptive wavelet image denoising method
is more effective for suppression of noisy image
with AWGN than others. Thus the image after
denoising have a better visual effect and preserve
the detail edges of image.
In the above research work they have made
the filtering with the combination of weiner filter
and wavelet transform, results with this are quite
better as compare to previous research but still we
have to improve the both parameters
4. PROPOSED WORK
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In the standard moving average filter the value at
the central pixel of the window is replaced by the
mean value of the corresponding input
neighborhood.
4.1. ATMED
Asymmetrical Triangular Median Filter (ATMED)
is a given neighborhood the filter takes into
account the deviation of the pixel value with the
median value and replaces the noisy pixel with a
fitting output based on fuzzy triangular
membership functions [9].The fuzzy filter with
triangular function and median value within a
window as the center value is given as,
O(x,y)
Where: Imax(x, y), Imin (x,y), and Imed (x,y) are the
maximum value, the minimum value and the median
value in the neighborhood [9].
4.2. ATMAV
Asymmetrical Triangular Moving Average Filter
(ATMAV) is a given neighborhood the filter takes
into account the deviation of the pixel value with
the mean value and replaces the noisy pixel with a
fitting output based on fuzzy triangular
membership functions [9].
O(x,y)
Where: IMAX(x, y), Imin (x, y), and Imed (x, y) are the
maximum value, the minimum value and the
median value in the neighborhood.
4.3. METHODOLOGY
First select an image, check, is it gray
image or color image? If color image then
firstly convert this image into gray image.
Then use it as input image.
The next step will be to apply wavelet
transform (DWT) to decompose the noisy
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International Journal of Engineering Trends and Technology (IJETT) – Volume 24 Number 2- June 2015
image into four sub images: LL, HL, LH,
and HH. After this adopt wiener filter for
LL sub image and apply thresholding to
remaining sub images.
After this step we apply median filter and
wiener filter with haar wavelet one by one.
Then reconstructs image by wavelet
inverse transform, and gets the denoise
image.
Fig 4: (a)
Fig 4: (b)
Finally, calculate PSNR between original
image and noisy image and RMSE
between the denoise image and original
image.[10]
5. COMPARATIVES RESULTS
The performance for denoising of image were
tested on set of grayscale images such as Lena
image, (512 512). Add the noise to the image
based on different values of variance. Perform
image denoising via wavelet [8] and wiener filter
and median filter with haar wavelet [9]. Table
shows the combination different methods (PSNR,
RMSE) at different noise level. The Wiener with
haar wavelet are giving the best denoising result.
Apart from this the comparison has been done
including Median filter and high performance filter
based on statistic methods for image processing.
Robustness and detail preservation are the two
most important aspects of modern image
enhancement filters. In this paper, we proposed a
new fuzzy-based adaptive algorithm that provides
robustness across a wide variation of high impulse
noise, without significant deterioration of fine
details of the original image.
Table2: Comparison of various Filters in terms of PSNR values
for corrupted “Lena” image [11]
Noise
variance
Median
Filters
HPFSM
0.01
34.44
42.82
119.42
120.50
0.02
34.14
40.21
76.89
80.60
0.03
33.78
38.18
50.129
60.50
0.04
33.21
36.78
49.235
50.40
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Wiener
Proposed
Fig 4: (c)
Fig 4: (d)
Figure 4: Resulting images from different noise
(a) Original image (b) median filter (c) HPFSM (d)
Wiener
6. CONCLUSION
Based on the comparative result, we conclude
that
The median filter with haar gives worst
result for image denoising.
HPFSM gives better results compare to
median filter.
The wiener filter with haar wavelet gives
good result as compared to median filter.
Thus we conclude that with haar wavelet
is better technique for image denoising.
7. REFERENCES
[1] R C Gonzalez and R .E.Wood Digital image processing
Prentice hall, upper saddle river, N .J.,2nd edition, 2002.
[2] Huipin Zhang,Aria Nosratinia and R. 0.Wells, “Image
Denoising Via Wavelet-Domain Spatially Adaptive FIR Wiener
Filtering”, IEEE Trans., pp.2179-2182, 2000.
[3] Xiwen Qin , Yang Yue, Xiaogang Dong and Xinmin Wang ,
ZhanSheng Tao “An Improved Method of Image Denoising
Based on Wavelet Transform” International Conference on
Computer, Mechatronics, Control and Electronic Engineering
(CMCE) 2010.
[4] Li Ke, Weiqi Yuan and Yang Xiao, “An Improved Wiener
Filtering Method in Wavelet Domain”, IEEE Trans., ICALIP,
pp.1527-1531, August 2008.
[5] Sachin D Ruikar and Dharmpal D Doye “Wavelet Based
Image Denoising Technique” (IJACSA) International Journal
of Advanced Computer Science and Applications, Vol. 2, No.3,
March 2011.
[6] Li Shixin, Zhang Xinghui and Wang Jianming “A new
Local Adaptive Wavelet Image De-noising Method”, IEEE
Computer Society, ISCCS, pp.154-156, 2011.
[7]https://www.clear.rice.edu/elec431/projects95/lords/wiener.ht
ml
[8] Nevine Jacob and Aline Martin “Image Denoising In the
Wavelet Domain Using Wiener Filtering” December 17, 2004.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 24 Number 2- June 2015
[9] Stefan Schulte, Valerie De Witte and Etienne E.Kerre, “ A
Fuzzy Noise Reduction Method For Color
Images” IEEE Transactions on image Processing, Vol 16, No.5,
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[10] Jin F,Fiegush, P,Winger L et al., “Adaptive Wiener filtering
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[11] Pao-Ta Yu*,1, Yui-Lang Chen1 “A High Performance Filter
Based on Statistic Methods for image processing “978-0-76953382-7/08 $25.00 © 2008 IEEE DOI 10.1109/ISDA.2008.34
[12] Madeena Sultana” High Density Impulse Denoising by A
Novel
adaptive fuzzy filter 978-1-4799-0400-6/13/$31.00
©2013 IEEE
ISSN: 2231-5381
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