An efficient image compression algorithm using dct biorthogonal wavelet transform with arithmetic coding

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 04 Issue: 02 | Feb-2015, Available @ http://www.ijret.org 94
AN EFFICIENT IMAGE COMPRESSION ALGORITHM USING DCT-
BIORTHOGONAL WAVELET TRANSFORM WITH ARITHMETIC
CODING
Priyatosh Halder1
1
Radar Section, Air Force Jodhpur, Rajasthan, India
Abstract
Recently the digital imaging applications is increasing significantly and it leads the requirement of effective image compression
techniques. Image compression removes the redundant information from an image. By using it we can able to store only the
necessary information which helps to reduce the transmission bandwidth, transmission time and storage size of image. This paper
proposed a new image compression technique using DCT-Biorthogonal Wavelet Transform with arithmetic coding for
improvement the visual quality of an image. It is a simple technique for getting better compression results. In this new algorithm
firstly Biorthogonal wavelet transform is applied and then 2D DCT-Biorthogonal wavelet transform is applied on each block of
the low frequency sub band. Finally, split all values from each transformed block and arithmetic coding is applied for image
compression.
Keywords: Arithmetic coding, Biorthogonal wavelet Transform, DCT, Image Compression.
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1. INTRODUCTION
Now a day, it is a great challenge to handle huge amount of
data due to explosive growth of multimedia and internet
technology. The data are in the various forms like graphics,
image, audio etc. This brings the problem at transmission
bandwidth, storage which leads the efficient compression.
Since last few years increasing the efforts on the embedded
wavelet coding algorithms [1-3]. Beside very good
compression performance it can also reconstruct a
reasonable good quality image. The image compression can
be divided into two types: lossy and lossless image
compression [4]. It is possible to recover the original image
by lossless compression whereas losses of some amount of
information occur in case of lossy compression. In many
applications lossy compression is preferred since it provides
large compression ratio [5].
Image compression can be obtained from the various types
of transformation techniques like DCT [6], DFT, DWT etc.
In traditional DCT based JPEG [7] compression system
represents image as a superposition of cosine function of
different discrete frequencies. The discrete cosine transform
(DCT) is a popular compression scheme because it can able
to give optimal performance and easily implemented with a
reasonable cost. So it is used in several compression
algorithms like JPEG for still images and MPEG [8] for
moving images. Many attempts have been taken for
improving the compression scheme [9, 10] by utilizing and
identifying the features within the images.
In any image compression algorithm there are three major
steps: transform and quantization, modeling and ordering
and finally entropy coding. In the transform step inter-pixel
redundancy reduces and energy compaction occurs. To
achieve better compression quantization, modeling and
ordering are used. In the final stage the quantized outputs
are sent to the entropy encoder. This step helps to generate
bit stream which represent efficient quantized output. In my
proposed method a new algorithm is investigated using
modeling and ordering in wavelet domain [11].
It is seen that many attempts has been taken to design an
efficient image coding techniques with which the geometry
of edge singularities of image is exploited. Over the past few
years, a number of image compression algorithms like EZW
[12], EBCOT [9], JPEG 2000 [13], GW [14] and SPHIT [7]
have introduced.
This paper can be represented in the following ways that: in
section II explains the review of literature. Section III
describes the proposed method of DCT-Biorthogonal
wavelet transform based image compression with arithmetic
coding. The results and analysis are represented in section
IV. Finally the section V contains the conclusion and future
work.
2. LITERATURE REVIEW
Ronald A. De Vore et al. in [15] explained a new image
compression method based on wavelet decompositions. This
theory relates a) the error between the original and
compressed image the rate of decay occurs as the size of the
compressed image representation increases b) in certain
smoothness classes the smoothness of the image called
Besov spaces. Within this theory, the error occurred by the
quantization of wavelet transform coefficients is described.
It is shown that wavelet-based methods are near optimal
within a larger class of stable transform based, nonlinear
methods of image compression possible if pictures can be

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characterized by their membership in the smoothness classes
considered here. Based on previous experimental research
on the spatial-frequency intensity response of the human
visual system, it is argued that in most instances the error
incurred in image compression should be measured in the
integral sense instead of the mean-square sense.
G.K. Kharate et al. in [16] described that the presently
wavelet packet and discrete wavelet transform has emerged
as popular techniques for image compression. The
comparison of compression performance of Biorthogonal,
Daubechies, Coiflets and other wavelets along with results
for different frequency images is presented here. Based on
the result, it can be concluded that proper selection of
mother wavelet on the basis of nature of images and
improves compression ratio and quality remarkably.
Sanjeev Pragada et at. in [17] described that current
denoising techniques which are used in the classical
orthonormal wavelets for decomposition of an image
corrupted with additive white Gaussian noise. For which
various thresholding strategies are built. Because of their
poor performance the use of available biorthogonal wavelets
in image denoising is less common. Here it is presented a
method to design image-matched biorthogonal wavelet
based on their potential for denoising. It is conducted
experiments on various image datasets namely Satellite,
Natural and Medical images with the designed wavelets
using two existing thresholding strategies. Here in the every
dataset the biorthogonal wavelets show an average
improvement of 35% in MSE for low SNR values (0 to
18db). This improvement was also seen in the visual
comparison and PSNR. This point has an importance of
matching when using wavelet-based denoising.
Han Sae Song et al. in [18] presented a new DCT-based
embedded image compression algorithm. From the ones in
the neighbouring blocks the magnitudes of DCT coefficients
are estimated and in the encoding the coefficients with
larger estimates are given higher priority. As contexts for
arithmetic coding this priority information is also used. This
method finds more significant coefficients as compare to the
conventional methods. Hence it provides higher coding gain.
Sunil Malviya et al. in [19] proposed a new scheme for
image compression using Discrete Wavelet Transform
taking into account sub-band features in frequency domains.
This method involves two steps firstly a two levels discrete
wavelet transforms on the selected input image. The original
images is decomposed at different 8x8 blocks and apply
Walsh-Wavelet Transform on each block of the low
frequency sub-band. Apply Arithmetic Coding on each sub-
band independently after dividing each sub-band by a factor.
Transform each block from LL2 and then divide each block
8x8 separated into DC value and finally compressed by
Arithmetic coding.
After thoroughly studying the different image compression
algorithms have been presented here, some missing
techniques come in my mind. This can be filled up by DCT-
Biorthogonal wavelet transform using arithmetic coding.
3. PROPOSED METHOD
The following steps represent the summarizing form of our
proposed method for image compression:
1. First select an input image from database.
2. Divide the image into 8x8 blocks.
3. Apply the Biorthogonal wavelet transform for
compression.
4. From the standard parameter set the quantization
factor parameters QF1 and QF2.
5. From the range 1-10 set the compression ratio factor.
6. Apply the DCT-Biorthogonal wavelet transform and
then use the arithmetic coding for compression.
Step 6 consists of the following steps:
i. Two level discrete Biorthogonal wavelet
transform.
ii. On each block of the low frequency sub-band
apply 2D DCT-Biorthogonal wavelet
transform.
iii. From each transform block 8x8 split all the
vlues.
iv. By using arithmetic coding compress each
sub-band. The first part of DCT-Biorthogonal
wavelet transform compression steps for high
frequency, domains and then second part of it
for low frequency.
7. From each transform block 8x8 split all DC values.
8. Use Arithmetic coding for compression of each sub-
band.
9. Finally by the compression output image is obtained.
Fig -1: Flow chart of proposed method

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The above figure shows the flow chart of proposed method.
Here firstly, an input image is taken and divide it into 8x8
blocks. Hence biorthogonal wavelet transform is applied on
it. The quantization factor and compression ratio is chosen
and DCT-biorthogonal wavelet transform is applied on 8x8
block low frequency sub-band. Then compress each sub-
band with the help of arithmetic coding and split DC values
of 8x8 blocks. Use arithmetic coding to compress each sub-
band and output image will get finally.
4. RESULTS AND ANALYSIS
Here as a dataset some classic image like Mandrill image,
Lena image and Barbara image is used. The size of the each
image is 256x256. The following figure 2 shows the
selected three classic images as a test image. Here for
compression biorthogonal 6.8 wavelet, value of each
quantization factor (QF1 and QF2) 0.02 and compression
ratio factor 2 is selected. For comparing the results of
proposed method with the existing methods the PSNR (in
dB) value is chosen.
Fig -2: Test Images
The following table 1 shows the comparison result of the
proposed algorithm and different existing method such as
EZW, EBCOT, JPEG 2000, GW and SPHIT for the above
mentioned three test images.
Table -1: Comparison of PSNR results
Methods
PSNR (in dB)
Mandrill Lena Barbara
EZW 32.23 30.38 28.54
EBCOT 31.96 28.58 29.36
JPEG 2000 31.90 29.58 30.96
GW 30.20 31.39 32.84
SPHIT 30.90 29.30 30.32
PROPOSED
METHOD
32.75 33.63 34.39
From the above table it is seen that using the proposed
method gives the PSNR results 32.75dB, 33.63 dB and
34.39 dB for the Mandrill image, Lena image and Barbara
image respectively. And for all cases the performance of the
proposed algorithm based on DCT-Biorthogonal wavelet
transform using arithmetic coding is better. The chart 1
shows the representation of the above results in the form of
bar graph.
Chart -1: Comparison of compression results (PSNR) of various methods

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From the chart 1 it is clear that the performance of the
proposed method is better than the existing EZW, EBCOT,
JPEG 2000, GW and SPHIT method.
5. CONCLUSION AND FUTURE WORK
This paper represents an image compression algorithm that
adopts DCT-Biorthogonal wavelets transform with the
arithmetic coding. This algorithm is applied on several types
of images. It is seen that this method removes the
redundancy from images and also it significantly reduces the
blocking artifacts and false contouring effects. This method
gives better results as compare to different existing
compression methods. However, the performance of this
method can be extended by using different wavelet and
different transform with various entropy encoding
techniques. In future some more efforts are required to give
on it as the image compression is still a challenging
problem.
ACKNOWLEDGEMENTS
I would like to thank to my friend Nalini Mittal who has
motivated me to complete this work. Special thanks to my
father who always supports my innovative ideas.
REFERENCES
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[19]. Sunil Malviya, Neelesh Gupta and Vibhanshu
Shirvastava, “2D-Discrete Walsh Wavelet Transform for
Image Compression with Arithmetic Coding”, 4th ICCCNT
- 2013 July 4 - 6, 2013, Tiruchengode, India
BIOGRAPHY
Priyatosh Halder received the M. Tech
degree in Electronics and
Communication Engineering from Sri
Sukhmani Institute of Engineering and
Technology, Dera Bassi (Punjab), India.
Presently he is working in Indian Air
Force. He is a member of IEEE and IEI. His research
interest is digital image processing.

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