Image Denoising of various images Using Wavelet Transform and Thresholding Techniques

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 02 | Feb -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 517
Image Denoising of Various Images using Wavelet Transform and
Thresholding Techniques
Yamini P. Chaudhari 1, Dr. P. M. Mahajan2
1ME Student, Dept. of Electronics and Telecommunication, J. T. Mahajan College of Engineering, Faizpur.
2Associate Professor, Dept. of Electronics and Telecommunication, J. T. Mahajan College of Engineering, Faizpur.
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Abstract - Generally the Gaussian and salt Pepper
noise occurred in images of different quality due to
random variation of pixel values. To denoise these images,
it is necessary to apply various filtering techniques. So far
there are lots of filtering methods proposed in literature
which includes the haar, sym4, and db4 Wavelet
Transform based soft and hard thresholding approach to
denoise such type of noisy images. This work analy-ses
exiting literature on haar, db4 and sym4 Wavelet
Transform for image denoising with variable size images
from self generated grayscale database generated from
various image sources such as satellite images(NASA),
Engineering Images and medical images. However this
new proposed Denoising method shows signs of
satisfactory performances with respect to previous
literature on standard indices like Signal-to-Noise Ratio
(SNR), Peak Signal to Noise Ratio (PSNR) and Mean
Square Error (MSE). Literature indicates that Wavelet
transform represents natural image better than any other
transformations. Therefore, Wavelet coeficient can be used
to improve quality of true image and from noise. The aim
of this work to eliminate the Gaussian and salt Pepper
noise in wavelet transform domain. Subsequently a soft
and hard threshold based denoising algorithm has been
developed. Finally, the denoised image was compared with
original image using some quantifying statistical indices
such as MSE, SNR and PSNR for different noise variance
which the experimental results demonstrate its
effectiveness over previous method.
Key Words: Image Denoising, Gaussian noise, salt
Pep-per noise, Wavelet transforms, Image
Thresholding techniques, Signal-to-Noise Ratio
(SNR), Peak Signal to Noise Ratio (PSNR), Mean
Square Error (MSE).
1. INTRODUCTION
The image usually has noise which is not easily
eliminated in image processing. According to actual
image characteristic, noise statistical property and
frequency spectrum distribution rule, people have
developed many methods of eliminating noises, which
approximately are divided into space and trans-
formation fields .The space field is data operation carried
on the original image, and processes the image grey
value, like neighborhood average method, wiener filter,
center value filter and so on. The transformation field is
management in the transformation field of images, and
the coefficients after trans-formation are processed.
Then the aim of eliminating noise is achieved by inverse
transformation, like wavelet transform [1], [2].
Successful exploitation of wavelet transform might
lessen the noise effect or even overcome it completely
[3]. There are two main types of wavelet transform -
continuous and discrete [2]. Because of computers
discrete nature, computer programs use the discrete
wavelet transform. The discrete transform is very
efficient from the computational point of view. In this
paper, we will mostly deal with the modeling of the
wavelet transform coefficients of natural images and its
application to the image denoising problem. The
denoising of a natural image corrupted by Gaussian noise
is a classic problem in signal processing [4]. The wavelet
transform has become an important tool for this problem
due to its energy com-paction property [5]. Indeed,
wavelets provide a framework for signal decomposition
in the form of a sequence of signals known as
approximation signals with decreasing resolution
supplemented by a sequence of additional touches called
details [6][7]. Denoising or estimation of functions,
involves reconstituting the signal as well as possible on
the basis of the observations of a useful signal corrupted
by noise [8] [9] [10] [11]. The methods based on wavelet
representations yield very simple algorithms that are
often more powerful and easy to work with than
traditional methods of function estimation [12]. It
consists of decomposing the observed signal into
wavelets and using thresholds to select the coefficients,
from which a signal is synthesized [5]. Image denoising
still remains a challenge for researchers because noise
removal introduces artifacts and causes blurring of the
images. This paper describes different methodologies for
noise reduction (or denoising) giving an insight as to

which algorithm should be used to find the most reliable
estimate of the original image data given its degraded
version.
2. REVIEW OF SELECTED LITERATURE ON WAVELET
TRANSFORM BASED IMAGE DENOISING
F. Xiaoa et al. [6] presented a technique Wavelet-
based image denoising which is the foundation of
wavelet-based de-noising through thresholding. To
explores properties of various thresholding techniques
in wavelets denoising several natural gray scale test
images like Lina, Barbara of size 512 X 512 at different
noise levels are 10, 20, 30, 35 with soft thresholding and
semi-soft thresholding with discrete Mayer filter having
4th level decomposition are used to evaluate these
threshold selection algorithms are used to explore
various Properties of image denoising algorithm and
quantitative comparison between these techniques
through MSE and PSNR (Peak Signal-to-Noise Ratio).
Based on their results authors conclude that BayesShrink
and Feature-Adaptive Shrink are the best wavelet-based
denoising methods in methods.
Z. Weipeng et al. [7] Presented method with combining
two-dimensional discrete wavelet transform and
bilateral denoising is introduced for this purpose two
images of coal-mine refuge chamber in different scenes
are selected as original images with sizes of 352 X 288
pixels. First the wavelet transform is adopted to break
down the image of safety enclosure and low frequency
component of subject image remains unchanged. Then, 3
high-frequency elements are activated by bilateral
filtering, and the image is reconstructed. While supplying
better optical effect and ultimately terminate that
integrating wavelet transform and bilateral filtering
collectively, can in effect destruct image noises of refuge
chamber, and result comparison given in this paper
depending on Comparison of information entropy,
standard deviation and mean gradient after applying
bilateral filtering based on wavelet transform. When coal
mine disaster happen proposed method will guide the
emergency deliverance and assurance the coal-mine
safety production.
C. chen et al. [8] proposed method which uses the
digital complex ridgelet transform to denoise some
standard images such as lina, MRI image and Thumb
Impression image having Gaussian white noise. Hard
thresholding of the complex ridgelet coefficients is used.
their experiment Results show that this new method
performs VisuShrink, the ordinary ridgelet image
denoising, and wiener2 filter both in terms of peak
signal-to-noise ratio and in visual quality. In particular,
this method preserves sharp edges better while
removing white noise. Complex ridgelets could be
applied to curvelet image denoising as well.
A. Jaiswal et al. [9]proposed a method worked with de-
noising of user generated image, saltpepper and
Gaussian noise. Remaining work is organized in four
steps first image is denoised by filtering method, second
images is denoised by wavelet based techniques using
thresholding, third hard thresholding and filtering
method applied simultaneously on noisy image, at last
results of PSNR (peak signal to noise ratio) and MSE
(mean square error) are calculated by comparing all
cases. Experiments are performed on the 512 X 512
noisy images with noise having noise variance 0.04,
output of median filter, Wiener filter, hard thresholding
and hard thresholding plus median filtering
implemented on the basis of PSNR, MSE and visual
quality of image. The filtering and wavelet thresholding
technique jointly gives good agreement of PSNR and MSE
than applying Bior, Hard thresholding plus Wiener filter
method.
G. Gao [10] proposed a method controls both the
structural and statistical belongings of microarray of
stranded images lina, barbras and Gaussian noise added
which acting for wavelet based microarray picture
denoising and for shrinking of microarray images. The
shrinking scheme is unusual in its use of approximate
(rather than perfect) textual matter. Proposed method
brings forth smaller overall bits per pixel when
compared with Micro Zip the best-known microarray
compression algorithm. Given the assets of data typically
bring forth by microarray based on experimentation.
Further granted the important amount of noise that is
ordinary in such experiments, method acting for
removing (or at least reducing) the noise, in front further
analysis using the microarray images.
H. Rabbani et. al [11] proposed denoising model is able
to capture the heavy-tailed nature of wavelet coefficients
and the local parameters model the intrascale
dependency between the coefficients. For that purpose
standard images are taken such as ship, mri and gausian
noise is added and proved a novel method for
image/video denoising based on designing a maximum a
posteriori (MAP) estimator, which relies on the mixture
distributions for each wavelet coefficient in each sub
band. This method employs two different versions of
expectation maximization (EM) algorithm to find the
parameters of mixture model and compare our new
method with other image denoising techniques that are
based on (1) non mixture pdfs that are not local, (2) non
mixture pdfs with local variances, (3) mixture pdfs

without local parameters and (4) methods that consider
both heavy-tailed and locality properties. The technique
is best among the best reported in the literature both
visually and peak signal-to-noise ratio (PSNR). Because
3-D complex wavelet transform provides a motion-based
multiscale decomposition for video, proposed algorithm
has very good performance without explicitly using
motion estimation.
V. Bruni et al. [12] Presents scheme for simultaneous
compression and denoising of images using WISDOW-
Comp (Wavelet based Image and Signal Denoising via
Overlapping Waves Compression). However, atoms can
be also used for achieving compression. In selected
images such as lina, ship etc the core of WISDOW-Comp
consists of recovering wavelet details by exploiting
wavelet low frequency information. Therefore, just the
approximation band and significance map of atoms
absolute maxima have to be encoded and sent to the
decoder for recovering a cleaner as well as compressed
version of the image such as lina. Results show that
WISDOW-Comp outperforms the state of the art of
compression based denoisers in terms of both rate and
distortion.
3. PROPOSED ALGORITHM
An image is a rectangular grid of pixels. It has a definite
height and a definite width counted in pixels. Each pixel
is square and has a fixed size on a given display.
However different computer monitors may use different
sized pixels and different types such as gray scale, color
image (.jpeg, .gif, .png, .tiff etc.). The noise will reduce the
quality of the images(the different noised images are
showed in Figure 3 such as Gaussian and salt pepper
noise) To clear noise from image is called as image
denoising one goal in image restoration or denoising is to
remove the noise from the image in such a way that the
original image is discernible of course, noise is in the eye
of the be holder; One approach is to decide that features
that exist on a very small scale in the image are noise,
and that removing these while maintaining larger
features might help clean things up. Different Wavelet
Transforms such as Db4, Sym4 and Haar used in project
work Daubechies constructed the first wavelet family of
scale functions that are orthogonal and have ignite
vanishing moments, i.e., compact support. This property
insures that the number of non-zero coefficients in the
associated filter is innate. This is very useful for local
analysis. The Haar wavelet is the simplest wavelet
transform. It is also the only symmetric wavelet in the
Daubechies family and the only one that has an explicit
expression in discrete form. Haar wavelets are related to
a mathematical operation called Haar transform such as
one of the brightest stars in the world of wavelet
research, invented what called compactly supported
orthonormal wavelets are thus making discrete wavelet
analysis practicable. The names of the Daubechies family
wavelets are written dbN, where N is the order [10], and
db the surname of the wavelet. Symlet Wavelet, also
known as “least asymmetric” wavelet, defines a family of
orthogonal wavelets. Symlet Wavelet[n] is defined for
any positive integer n. The scaling function (Ψ) and
wavelet function (Φ) have compact support length of 2n.
The scaling function has n vanishing moments. Symlet
Wavelet can be used with such functions as Discrete
Wavelet Transform and Wavelet Phi, etc. In symN, N is
the order. Some author’s use 2N instead of N.
Thresholding is the simplest method of image denoising.
In this from a gray scale image, thresholding can be used
to create binary image. Thresholding is used to segment
an image by setting all pixels whose intensity values are
above a threshold to a foreground value and all the
remaining pixels to a background value. Thresholding is
mainly divided into two categories hard and soft
thresholding.
Image processing is required to remove
unwanted noise so that the quality of the processed
image does not deteriorate. Generally, the noise is
removed using some specified filters. Several methods
have been reported to remove such noises form the
stationary digital images. Discrete wavelet transform
(DWT) is one of the recent wavelet transforms used in
image processing. DWT decomposes an image into
different sub images as shown in figure below.
Figure 1: First and Second level of Image decomposition.
Denoising algorithm using DWT requires the
decomposition of noised images to get the wavelet
coefficients [9]. These coefficients are then denoised
with wavelet threshold. Finally, inverse transform is
applied to the coefficients and get denoised image [9].

This process is called the reconstruction of an image
using decomposition.
3.1 Image Denoising using Wavelet and
Thresholding is carried out in following steps.
To denoise the image by using wavelet transform, the
following steps are carried out as per algorithm shown in
figure 2, For the experimentation variable size images
from various image sources such as satellite
images(NASA), Engineering Images and medical images
are taken in to consideration.
Step 1: Select any one original image from MATLAB
database for example original lina image from database
is selected as shown in figure 3.
Step 2: Guassian noise at the variance of 0.01 or salt
peeper noise at the variance of 0.1 is added in to original
lina image from wavelet toolbox for example Gaussian
noise of variance 0.01 and Salt pepper noise of variance
0.1 is added in to selected image from wavelet toolbox as
shown in figure 4.
Step 3: These Noisy images are decomposed using
different wavelet transforms such as db4, haar and sym4
for example haar Wavelet Transform is applied to these
noisy images
Step 4: First level or second level decomposition is
applied to these noisy image. In the first level of
decomposition, the image is split into 4 sub bands,
namely the HH, HL, LH and LL sub bands. The HH sub
band gives the diagonal details of the image; the HL and
LH sub bands give the horizontal and vertical features
respectively. The LL sub band is the low resolution
residual consists of low frequency components and its
sub bands are further split at higher levels of
decomposition as shown in figure 1. In Wavelet Sub
bands as the level increases the coefficients of sub band
becomes smoother.HL2 is smoother than HL1 and so
threshold value should be smaller than for HL1 for
example first and second level of decomposition for lina
image is shown in figure 6.
Step 5: We have performed Soft and Hard Thresholding
at each decomposition level of an image for different
wavelet transforms. At each level the value of threshold
is different for example at the end the inverse of the
wavelet transform has been performed to get the
denoised image as shown in figure 7.
Step 6: Finally the inverse of the wavelet transform has
been performed to get the denoised image as shown in
figure 7 and The performance of various wavelet
transforms has been compared with the help of various
parameters such as Peak signal to Noise Ratio (PSNR),
Signal to Noise Ratio (SNR) and Mean Square Error
(MSE), figure 8 shows complete denoised step wise
result for lina.
Figure 2: Wavelet Denoising Algorithm form Haar, Db4
and Sym4.
Figure 3: Selected original lina Image from MATLB
database.
Figure 4: Noisy lina Image a) lina with AWGN .01
varience and b) lina with Salt Peeper .1 variance.
4. EXPERIMENTAL RESULT AND DISCUSSION
Two parameters, PSNR (peak signal to noise ratio) and
MSE (Mean square Error) are calculated for all the
denoised images.
4.1 Mean Square Error (MSE):
Mean Square Error (MSE) is defining as the
average of square of the error. Error is difference
between desire quantity and estimated quantity. The
Mean Square Error (MSE) provides a means of choosing
the best estimator. We also calculate Root Mean Square
Deviation taking the square root of Mean Square Error
(MSE), it is also good statistic parameter for measure

quality of image. Having a Mean Square Error of zero (0)
is ideal. Lower the MSE produces good denoising result,
The Mean Square Error (MSE) is defined and used to
calculate error metrics used to compare the various
image compression techniques are the Mean Square
Error (MSE).
Where f (i,j) is the original image, F (i,j) is the
approximated version (which is actually the
decompressed image) and N or M are the dimensions of
the images.
Figure 5: Level of decomposition a) lina with 1st
level of decomposition b) lina with 2nd level of
decomposition.
Figure 6: lina Image a) Soft thresholding with 1st level
Decomposition b) Hard thresholding with 1st level
Decomposition c) Soft thresholding with 2nd level
Decomposition d) Hard thresholding with 2nd level
Decomposition.
Figure 7: Denoised lina Images a and b) with 1st level
Decomposition c and d) with 2nd level decomposition.
Figure 8: Result of AWGN noisy lina using haar second
level Decomposition with Soft thresholding.
4.2 Peak Signal to Noise Ratio (PSNR):
The Peak Signal-to-Noise Ratio (PSNR) is
defined as a ratio between the maximum possible
power of a signal and the noise power that affects
the fidelity of its representation. PSNR is usually
expressed in terms of the logarithmic decibel scale.
The PSNR is most commonly used as a measure of
quality of reconstruction of lossy compression for
image compression. It is most easily defined via the
Mean Square Error (MSE) which for two mxn
monochrome images i and k where one of the
images is considered a noisy approximation. Two of
the error metrics used to compare the various
image compression techniques are the Mean Square
Error (MSE) and the Peak Signal to Noise Ratio
(PSNR). The MSE is the cumulative squared error
between the compressed and the original image,
whereas PSNR is a measure of the peak error. The
mathematical formulae for the two are:
The PSNR is defined as:
Here, MAXI is the maximum possible pixel value of the
image. When the pixels are represented using 8 bits per
sample, this is 255. More generally, when samples are
represented using linear PCM with B bits per sample,
MAXI is . Higher Peak signal to noise ratio
produces good denoising results. Above figure 9 and
figure 10 shows that Different Values of MSE and PSNR

for Selected images such as lina, Barbara, cameraman,
Runner and Handshake, Grayscale Images with variable
sizes are used for experimentation. Using proposed
algorithm it is clear that PSNR values are not same for
haar, db4 and sym4 wavelet transform. Out of these
three sym4 shows high PSNR and Lowest MSE vales.
Figure 9: MSE Values of selected 5 Images with Hard and
Soft Thresholding and First and Second Level of
Decomposition.
5. CONCLUSION
In this paper several well known algorithms for
denoising natural images were investigated and
their performance was comparatively assessed. A
new algorithm based on the haar, db4 and sym4
wavelet transform was developed. Its performance
was shown to be competitive with or exceeding the
performance of other algorithms. In addition, it has
been shown to the advantage of implementation
simplicity. There are different types of noises that
may corrupt a natural image in real life, such as
Gaussian noise and salt pepper noise etc. However,
both salt pepper and white Gaussian noise was
considered because of its simplicity. A major part of
the thesis was devoted to the review,
implementation and performance assessment of
published image denoising algorithms based on
various techniques including the haar, db4 and
sym4 Wavelet transform. The Wavelet transform
and its characteristics were studied and as per
result and comparison, and previous literature say
lower MSE of images gives good denoising result
mean clear denoised image and higher PSNR values
produces good quality of decomposed image it is
conduced that out of three haar db4 and sym4
wavelet transform sym4 gives lowest MSE values
(0.0373) for the different images and highest PSNR
value (62.4179) as compared to haar and db4.
Figure 10: PSNR Values of selected 5 Images with Hard
and Soft Thresholding and First and Second Level of
Decomposition.
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