IMAGE DENOISING BY MEDIAN FILTER IN WAVELET DOMAIN

The International Journal of Multimedia & Its Applications (IJMA) Vol.9, No.1, February 2017
DOI : 10.5121/ijma.2017.9104 31
IMAGE DENOISING BY MEDIAN FILTER IN
WAVELET DOMAIN
Afrah Ramadhan1
, Firas Mahmood2
and Atilla Elci3
1
Dept. of Electrical - Electronics Engineering, Aksaray University, Aksaray, Turkey
2
Technical College of Engineering, Duhok Polytechnic University, Duhok, Iraq
3
Dept. of Electrical - Electronics Engineering, Aksaray University, Aksaray, Turkey
ABSTRACT
The details of an image with noise may be restored by removing noise through a suitable image de-noising
method. In this research, a new method of image de-noising based on using median filter (MF) in the
wavelet domain is proposed and tested. Various types of wavelet transform filters are used in conjunction
with median filter in experimenting with the proposed approach in order to obtain better results for image
de-noising process, and, consequently to select the best suited filter. Wavelet transform working on the
frequencies of sub-bands split from an image is a powerful method for analysis of images. According to this
experimental work, the proposed method presents better results than using only wavelet transform or
median filter alone. The MSE and PSNR values are used for measuring the improvement in de-noised
images.
KEYWORDS
AGN; Noisy image; Median filter (MF); DWT; PSNR; Threshold.
1. INTRODUCTION
The need for efficient image de-noising techniques has grown with the huge production of digital
images. No matter how good cameras are, image improvement is often desirable to extend their
range of action [2]. A digital image is often corrupted by some noise native in the production
process and equipment, or injected into the image during its transmission. There are different
types of noise appearing in images, such as impulse noise, uniform noise, Salt-and-Pepper and
additive Gaussian noise [2, 3, 6]. Noise is present in an image either in an additive or
multiplicative form [11] as formulated below:
Additive noise : w (x, y) = s (x, y) + n (x, y)
Multiplicative noise : w (x, y) = s (x, y) × n (x, y)
where s(x,y) is the original image, n(x,y) is the noise introduced into the image producing the
corrupted image w(x, y), and (x,y) represents the pixel location [10,11,12]. Figure 1 shows the de-
noising concept by applied linear operation noise n(x,y) added to the image s(x,y) to form the
noisy image w(x,y), then applied de-noising technique to produce the restored image z(x,y).
Figure 1: Noising and de-noising concept.

32
The best way to test the effect of noise on a standard digital image is to insert Additive Gaussian
Noise AGN [2] as the possibility of seeing this type of noise in real life images is greater than
other types [2, 3]. AGN is used in this research; and, noisy image with AGN becomes more
difficult during image de-noising process.
The Gaussian noise is defined by the following probability density function F of Gaussian
random variable in Eq. 1 [10, 11, 12].
= √
… 1 [8]
where:
g : gray level
m : mean or average of the function
σ2 : variance of the noise
The proposed de-noising scheme is being introduced in the following section; its four variations
also considered in search of excellence. Section 3 takes up experimental testing of the proposed
schemes. Section 4 provides discussion and Section 5 conclusions.
2. PROPOSED DE-NOISING SCHEME
In digital image processing, de-noising technique used in order to reduce, or if possible remove,
noise without losing detail. There are various de-noising techniques. Gaussian noise can be
reduced using a spatial filter. While smoothing an image, the blurring of fine-scaled image edges
and details is possible for they correspond to the high frequencies blocked by the process. Among
the spatial filtering techniques conventionally employed for noise removal are mean
(convolution) filtering, median filtering and Gaussian smoothing. Most of the standard algorithms
used for de-noising perform an individual filtering process. The result decreases the noise, but the
image is blurred or smoothed at lines and edges due to high frequency losses.
In order to effectively reduce the noise with minimum adverse outcome, this research examines
employing various filters and wavelet transform in analyzing a digital image in useful sub-bands.
Wavelet transform and filtering, as well as a median filter are widely used individually for image
de-noising. In this work, we explore combinations that would produce better outcome for digital
image de-noising.
Digital image de-noising using Discrete Wavelet Transform (DWT) approach is being highlighted
in the following steps:
1. Apply DWT on the noisy image to split it into four sub-bands (A, H, V, D) by using
wavelet filter families [6, 4].
2. Choose one of the suitable threshold rule methods to compute a threshold value for each
one of the detail bands H, V, D.
3. Compare pixels in the sub-bands (H, V, D) against the specific threshold value for that
band. Set the pixel to zero if its value is less than the threshold of the band; otherwise,
test the next pixel value. This step gets repeated for all the pixels of the selected sub-
band.
4. Apply inverse DWT (IDWT) on the sub-bands to obtain the de-noisy (de-noised) image.
5. Apply median filter within WT alone before threshold or after threshold as needed by in
each case. Median filter follow the moving window principle. A 3×3 filter mask of pixels
is scanned over pixel matrix of the entire image, sorting all the values of the pixel from

33
the surrounding neighborhood in an ascending manner. Exchange the pixel with the
middle pixel value [3].
6. Compare the de-noised and the original image by computing the image quality of the de-
noising technique. The result expressed as the values of the Mean Square Error (MSE)
and the Peak Signal to Noise Ratio (PSNR). MSE and PSNR values are computed using
the equations 2 and 3 respectively [13, 14].
=
.
∑ ∑ , − , !"#$"# ………………... 2
% &' = 10. *+ #
,-.
/0
..........................3
where:
I (i, j) : original image
F (i, j) : de-noised image
M and N: size of the original image
max : maximum pixel value of grayscale image that is used in this work which equals to 255.
Thresholding is a simple and effective method of image segmentation used to generate digital
images from a grayscale image. As such, threshold technique is used beneficially for digital
image de-noising. Threshold technique is used in this study in digital wavelet domain. As it is
also dependent on the capabilities of wavelet transform for removing noise, the best choice of
threshold value would provide great de-noising [3, 7]. The selection of the threshold value is an
important factor for it determines which pixel values are to be kept or deleted in a sub-band. In
this study one level of DWT decomposition is applied and the threshold value is compared
against all the pixels at each detail bands (H, V, and D). Therefore, a good threshold value would
lead to less distortion of the image [3, 5, 7].
Threshold value is computed by applying the equation 4 as follows:
1ℎ =
3
……….. 4
Where:
σ : the noise value of noisy image, which is computed by using Robust Median Estimator
estimated from the sub-band HH by equation 5 below.
4 = 5 6 78 |: , | /0.6745 ............…….. 5
4. : is the standard deviation (STD) of the sub-bands, computed in the equation 6 [8].
4 = @
∑ .$ ,A B
CDE
F
………….. 6
Where:
: The standard deviation (STD)
m : the mean
n : the number of pixels in the sub-bands
xi : sub-band.
Threshold plays a major role in removal of noise from images because de-noising most frequently
produces smoothed images, also reducing their sharpness [7, 9, 15]. Table 1 displays the
estimated values of noise ratio, obtained by applying equation 5 at various noise levels.

34
Table 1: Estimated values of the noise ratio for sample images using HH sub-band (results of applying
Robust Median Estimator)
In this paper, two algorithms are considered for digital image de-noising based on using median
filter combined with DWT: the two classic de-noising methods depending on applying the DWT
only or the median filter only and mixing between the two techniques. In the following, the flow
diagrams illustrate each test case of the image de-noising methods. According to the analysis of
these sub-bands, digital image de-noising algorithm is applicable on the following four cases.
2.1. THE FIRST CASE: APPLYING DWT ONLY
In this case, only DWT is applied as de-noising technique in order to obtain sub-bands
(Approximation band, A, and detail bands H, V, and D). Equation 5 is used to estimate the noise
in the sub-band D, equation 6 is used to determine standard deviation for the detail sub-bands,
then equation 4 is used to find the threshold value for each sub-band. Pixel values of each sub-
band are compared against the band threshold value. If the pixel value is greater than the
threshold value, then it is set to zero. Otherwise, next pixel is processed (see equation 7). This
process is repeated until all the pixels are handled. At this time, IDWT is applied on de-noised
sub-bands. MSE and PSNR values are computed using equations 2 and 3 on the de-noised and the
original images. A block diagram of the process flow for this case is being displayed in Figure 2.
Figure 2: The block diagram for the first case, DWT only
2.2. THE SECOND CASE: APPLYING MEDIAN FILTER ONLY
In this case, only median filter is used to apply de-noising technique on the noisy image,
consequently obtaining the de-noised image then calculate MSE and PSNR as in case one. Figure
3 shows the block diagram for this second proposed method.
Figure 3: The block diagram for the second case, Median filter only

35
2.3. THE THIRD CASE: APPLYING MEDIAN FILTER BEFORE COMPUTING THE
THRESHOLD VALUE
In this case, DWT is applied on the noisy image to obtain detail sub-bands. Then, the median
filter is applied on each sub-band independently using the equations 4, 5 and 6. Then IDWT,
MSE and PSNR are calculated as in case one. Figure 4 shows the block diagram for the third
case, Median filter before threshold.
Figure 4: The block diagram for the third case, median filter before threshold.
2.4. THE FOURTH CASE: APPLYING MEDIAN FILTER AFTER COMPUTING THE
THRESHOLD VALUE
In this case, median filter is applied after computing the threshold value. All steps are as in case
one, except the Median filter is applied on the sub-bands after applying threshold value and
before the IDWT. Finally, MSE and PSNR values are computed as before. Figure 5 shows the
block diagram for the fourth case, Median filter after threshold.
Figure 4: The block diagram for the fourth case, median filter after threshold.
3. EXPERIMENTAL RESULTS
The above-mentioned cases of the proposed methods were implemented in MATLAB (R2015a).
In this implementation of the algorithm and running the subsequent tests, five standard sample
grayscale images sized 256×256 pixels each were used in generating the noisy images. The noise
type was Additive Gaussian Noise (AGN) with zero mean (m=0) and the noise intensity values
ranging from σ=15, σ=20, and σ=25. The ratio of the additive noise in the noisy image content
was unknown by the image de-noising method. For this reason, the Robust Median Estimator was
use in order to estimate the amount of noise in the image by the equation 5 [1].
Then, the standard deviation of each sub-band was computed to use it in equation 4 in order to
calculate the threshold value for each sub-band by using equation 7 as follows:

36







 ≥
=
otherwise
ThFjiF
jiF
,0
),,(
),('
.............. (7)
Where:
),( jiF : The pixel value of noisy image band.
),(' jiF : The pixel value of de-noised image.
Th : The threshold value.
To calculate the PSNR values, firstly the de-noised image was generated by applying IDWT on
the de-noised sub-bands. Such IDWT use was part of all proposed cases above except the
second one. The sample original images were Lena, Barbara, Camera, Fruits, and Butterfly.
Upon adding AGN in different levels to the original image, and by applying DWT with one
stage of analysis on noisy image to obtain high frequency sub-bands HH, HL and LH, in all four
cases, the results of the PSNR values are shown in Table 2. Corresponding images are being
displayed in Figures 5-9 below.
Table 2: PSNR values for four cases with different noise levels.
Figure 5: Result of the best PSNR value on de-nosing Lena image by median filter only and applying
median filter before threshold, (a) original image (b1,b2,b3) noisy image corrupted by noise ratio=15,20,25

37
respectively,(c1,c2,c3) de-noising by median filter only,(d1,d2,d3) de-nosing by applying median filter
before threshold
Figure 6: Result of the best PSNR value on de-nosing Barbara image by median filter only and applying
median filter before threshold, (a) original image , (b1,b2,b3) noisy image that corrupted by noise
ratio=15,20,25 respectively,(c1,c2,c3) de-noising by median filter only,(d1,d2,d3) de-nosing by applying
median filter before threshold.
Figure 7: Result of the best PSNR value on de-nosing Camera image by median filter only and applying
median filter before threshold

38
Figure 8: Result of the best PSNR value on de-nosing Fruits image by median filter only and applying
Figure 9: Result of the best PSNR value on de-nosing Butterfly image by median filter only and applying
median filter before threshold, (a) original image (b1,b2,b3) noisy image that corrupted by noise
4. DISCUSSION
The summary of the comparative analysis of PSNR values for five tested images, namely Lena,
Barbara, Camera, Fruits and Butterfly, at different level noises, are being displayed in table 2 and
the images themselves in figures 5,6,7,8, and 9. The efficiency of the proposed de-noising
methods was dependent on the nature of the image; for example, applying only median filter has a
good effect on Lena, Camera and Fruits images. Their images reveal a smooth texture. However,
the proposed methods of applying median filter before and after threshold on Barbara and
Butterfly produces coarse texture images. Therefore, median filter before and after threshold have
a better performance and efficiency than applying DWT only, which showed a poor effect
compared with other methods. This finding is in agreement with Kumar and Agarwal [10]. We

39
concluded that hybrid filter provides clear images and visually better quality. The mix between
using DWT and the median filter have shown significant results and they were able to recover
much more detail of the original image, providing a successful way of image de-noising. This
finding was consistent with the previous study by Shukla et al [16].
5. CONCLUSIONS AND FUTURE WORK
In this research, a new method of image de-noising is proposed. The proposed method employs
median filter and adaptive wavelet threshold, using different types of wavelet transform filters. It
achieves better PSNR values compared to that of applying DWT or median filter only. The
quality of images produced using the proposed de-noising method on the images corrupted with
Gaussian noise was compared in terms of PSNR against classic methods for DWT and the median
filter each alone. According to experimental results, the proposed method presents best values of
PSNR for the de-noised images. The robust median estimator was used to estimate the noise ratio
in the noisy images.
In the future, the proposed method can be modified by using more accurate estimation function
and other kinds of threshold methods in trying to improve its ability at image de-noising process.
REFERENCES
[1] Liu, Y. (2015). Image De-noising Method based on Threshold, Wavelet Transform and Genetic
Algorithm. International Journal of Signal Processing, Image Processing and Pattern Recognition,
8(2), 29-40.
[2] Kaur, G., & Kaur, R. (2012). Image De-noising Using Wavelet Transform and Various Filters.
International Journal of Research in Computer Science, 2(2), 15.
[3] Charde, M. P. (2013). A Review on Image De-noising Using Wavelet Transform and Median Filter
over AWGN Channel. Vol. 1, 44-47
[4] Burrus C.S., Gopinath R.A., Guo H. (1998). Introduction to Wavelets and Wavelet Transforms: A
Primer. Prentice Hall, USA, 281p.
[5] Toufik, B., & M Okhtar, N. (2012). The Wavelet Transform for Image Processing Applications.
INTECH Open Access Publisher. 396-422
[6] Ergen, B. (2012). Signal and image de-noising using wavelet transform. INTECH Open Access
Publisher. pp 496-514
[7] Om, H., & Biswas, M. (2012). An improved image de-noising method based on wavelet thresholding.
Journal of Signal and Information Processing, Vol. 3 No. 1, 2012, pp. 109-116
[8] Chang, S. G., Yu, B., & Vetterli, M. (2000). Adaptive wavelet thresholding for image de-noising and
compression. IEEE transactions on image processing, 9(9), 1532-1546.
[9] Hedaoo, P., & Godbole, S. S. (2011). Wavelet thresholding approach for image de-noising.
International Journal of Network Security & Its Applications (IJNSA), 3(4), 16-21.
[10] Kumar, P., & Agarwal, S. K. (2015). A Color Image Denoising By Hybrid Filter for Mixed Noise.
Journal of Current Engineering and Technology, 5(3). 1565-1572
[11] Saxena, C., & Kourav, D. (2014). Noises and Image De-noising Techniques: A Brief Survey.
International Journal of Emerging Technology and Advanced Engineering, 4(3), 878-885.
[12] Gupta, B., & Negi, S. S. (2013). Image Denoising with Linear and Non-Linear Filters: A Review.
International Journal of Computer Science, 10(2), 149-144.
[13] Qian, W. (2015). Research on Image De-noising with an Improved Wavelet Threshold Algorithm.
International Journal of Signal Processing, Image Processing and Pattern Recognition, 8(9), 257-266.
[14] Tai-sheng, Z. (2015). Research on Image Denoising with Wavelet Transform and Finite Element
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[15] Ismael, S. H., Mustafa, F. M., & Okümüs, I. T. (2016, March). A New Approach of Image Denoising
Based on Discrete Wavelet Transform. In Computer Applications & Research (WSCAR), 2016 World
Symposium on (pp. 36-40). IEEE.
[16] Shukla, H. S., Kumar, N., & Tripathi, R. P. (2014). Median Filter based Wavelet Transform for
Multilevel Noise. International Journal of Computer Applications, 107(14).

AUTHORS
Afrah Ramadhan master's student in Department of Electrical
Engineering at Aksaray University Aksaray, Turkey
Dr. Firas Mahmood Al-Fiky, received his BSc, MSc and PhD degrees from University
of Mosul-Iraq, College of Engineering, Electric dept. at 1997, 2000 and 2007 respectively.
He has a PhD in Computer Engineering, he is lecturer since 2007. He started teach
supervising post graduate courses since 2009 and until now. He is a head of
petrochemical engineer in Duhok Polytechnic University (DPU).
Atilla Elçi is full professor and the chairman of Department of Electrical
Computer Engineering at Aksaray University since August 2012. He has served in
Computer Engineering departments in various universities including METU, Turkey and
EMU, TRNC, since 1976. His professional practice includes the International
Telecommunication Union (ITU), Switzerland, as chief technical advisor for field projects
on computerization of telecommunication administrations of member countries (1985
and Information Technology & Telecommunications Pvt Ltd as founder/managing director, Turkey (1997
2003). He has organized IEEE COMPSAC & ESAS since 2006, SIN Conferences since 2007; IJRCS
Symposiums 2008-9, ICPCA_SWS 2012 and, LightSec 2016. He has published over a hundred journal and
conference papers and book chapters; co
Processes (LAP Lambert, 2011); edited the Semantic Agent Systems (Springer, 2011), Theory and Practice
of Cryptography Solutions for Secure Information Systems (IGI Global, 2013), The Handbook of Applied
Learning Theory and Design in Modern Education (IGI Global, 2016), Metacognition and Successful
Learning Strategies in Higher Education (IGI Global, 2017) and the proceedings of SIN Conferences 2007
16 (ACM), ESAS 2006-16 (IEEE CS). He is an associate editor of Expert Systems: The J
Knowledge Engineering and editorial board member of MTAP, JSCI, IJAS, IJISS, and guest editor for
several other journals. He has delivered several keynote/invited talks and served as reviewer for numerous
conferences.
master's student in Department of Electrical-Electronics and Computer
Engineering at Aksaray University Aksaray, Turkey
, received his BSc, MSc and PhD degrees from University
Iraq, College of Engineering, Electric dept. at 1997, 2000 and 2007 respectively.
He has a PhD in Computer Engineering, he is lecturer since 2007. He started teaching and
supervising post graduate courses since 2009 and until now. He is a head of
petrochemical engineer in Duhok Polytechnic University (DPU).
is full professor and the chairman of Department of Electrical-Electronics and
ngineering at Aksaray University since August 2012. He has served in
Computer Engineering departments in various universities including METU, Turkey and
EMU, TRNC, since 1976. His professional practice includes the International
U), Switzerland, as chief technical advisor for field projects
on computerization of telecommunication administrations of member countries (1985-97)
and Information Technology & Telecommunications Pvt Ltd as founder/managing director, Turkey (1997
e has organized IEEE COMPSAC & ESAS since 2006, SIN Conferences since 2007; IJRCS
9, ICPCA_SWS 2012 and, LightSec 2016. He has published over a hundred journal and
conference papers and book chapters; co-authored a book titled The Composition of OWL-S based Atomic
in Modern Education (IGI Global, 2016), Metacognition and Successful
Learning Strategies in Higher Education (IGI Global, 2017) and the proceedings of SIN Conferences 2007
16 (IEEE CS). He is an associate editor of Expert Systems: The J
40
and Information Technology & Telecommunications Pvt Ltd as founder/managing director, Turkey (1997-
e has organized IEEE COMPSAC & ESAS since 2006, SIN Conferences since 2007; IJRCS
9, ICPCA_SWS 2012 and, LightSec 2016. He has published over a hundred journal and
S based Atomic
in Modern Education (IGI Global, 2016), Metacognition and Successful
Learning Strategies in Higher Education (IGI Global, 2017) and the proceedings of SIN Conferences 2007-
16 (IEEE CS). He is an associate editor of Expert Systems: The Journal of

IMAGE DENOISING BY MEDIAN FILTER IN WAVELET DOMAIN

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