Wavelet, Wavelet Image Compression, STW, SPIHT, MATLAB

Presentation
on
A Comparative Study Of SPIHT And STW Compression Techniques
Using Wavelet Tool In Matlab
Sunday, May 16, 2021 Department of Mathematics and Computer Science, RDVV 1
Prepared By
Manish Tiwari
Student, M. Phil.,
Department of Mathematics and Computer Science,
RDVV, Jabalpur, MP.

Briefing of Dissertation
Introduction
Heisenberg Uncertainty Principle
Wavelet
MATLAB (Implementation Technique)
MSE, PSNR and CR
Result Comparison
Future Work
Conclusion
References
Index

The dissertation has been divided into three chapter:
Chapter – 1:
This chapter contains brief coverage of the research work. I
have given the basic definition related image processing.
Chapter – II:
This chapter contain, general introduction and basic image
processing. Preliminaries contain short definitions of points
which are very useful for our subject understanding and
normally confuses.
Chapter – III:
This chapter contains experiments, result and their analysis.
Experiments are performs using Wavelet Tool of MATLAB
software. This chapter also contain application of work, future
scope and conclusion of the work.
Briefing of Dissertation:

“A picture is worth more than ten thousand word”
Now days, transferring image data via computer networks and
portable storage devices is a very common practice.
To improve the quality of image, computers need to store
much information. If the image quality is low means less
information needed to store while the high image quality need to
store more information is in the computer.
These high quality image data needs much resources it became
a challenge to transport these image fast with minimum resource
utilization. To achieve the goal image compression techniques
are used.
Image compression means reduce the size of original image
and also maintain image quality [Gonzalez, 2002].
Introduction:

In Lossy Compression, image can not regain its original state
once it is compressed.
In Lossless Compression, image can regain its original state
from compressed image.
There are various techniques to compress images some of
them are Fourier transformation, STFT, wavelet etc.
Application of wavelet in image compression is one of the
dynamic, hot and popular concepts.
Introduction:

Heisenberg Uncertainty principle was stated in physics and claims
that it is impossible to know both the position and momentum of
particle simultaneously. In terms of signal, principle is given by the
rule that it is impossible to know both frequency and time at which
they occur. A signal can be localize in time or frequency but not
both simultaneous [Jayaraman et al., 2010].
Heisenberg Uncertainty Principle :

Wavelet:
Wavelet is functions that satisfy certain requirement. The
very name wavelet comes from the requirement that they
should integrate to zero waving above and below the x-axis.
Like sinusoidal in Fourier analysis, wavelet are used as basis
function in representing other function. Once the wavelet is
fixed. One can form of translation and dilation of the mother
wavelet [Vidaknovic, 1991].

Comprative Parameters:
PSNR: Stand for Peak Signal to Noise Ratio. The ratio is often used as a
quality measurement between original image and compressed image.
The higher PNSR better the quality of the compressed or reconstructed
image [Nema et al., 2012].
MSE: Stands for Mean Square Error. This represents the cumulative
squared error between the compressed and original image. The lower the
value of MSE, the lower the error [Mathworks, 2014].
CR: Stand for Compression Ration. Compression ratio is a ratio of non-
zero element of original matrices and transformed matrix. Every image is
a representation of bits. These bits are arranged in the matrix form. In
the comparison, we basically compare the bits were used to represent the
image of original and compressed image [Nema et al., 2012].
Compression Ration = original image/compressed image

MATLAB (Implementation Technique:
1. MATLAB Icon is clicked for executing MATLAB software
2. Once Screen is open, MATLAB start button will be clicked and
Toolbox icon is selected (it contains sub tool box).
3. Wavelet Toolbox Main Menu is selected as shown through
snapshot.

Implementation Method:
4. Once Screen is open, MATLAB start button will be clicked and
Toolbox icon is selected (it contains sub tool box).
5. True Compression 2-D button is shown in section Specialized
Tools 2-D. FIGURE , shows the different parameters, which can
be manipulated for image compression.

6. Parameters Wavelet, Level, Compression Method, color conversion
and Nb. Encoding loops are needed to select from available list of
parameters. Decomposition parameters value for Wavelet parameter is
selected as Haar wavelet and level parameter is select as 1. Value of
Color Conversion is none and the value Nb. Encoding loops is 8 both
are default.
7. Once parametric values for decomposition is select, decompose
button will be clicked. This is decompose the image according Haar
wavelet and level.
8. Now the compression method (SPIHT) is selected.
9. After selecting the compression method, the Compress button is
clicked for generating the output as shown

Result Comparison:
Original Images

Level – 1 SPIHT STW

Level - 3 SPIHT STW

Result Table (Black and White) SPIHT :
Levels MSE PSNR CR Size(KB)
1 8.161 39.01 98.95 11
2 15.65 36.19 39.74 10
3 39.161 32.12 15.80 9
4 83.51 28.91 6.51 8
5 165.1 25.95 3.00 7
6 332.8 22.91 1.34 5
7 332.7 22.91 1.28 5
8 641.6 20.06 0.53 4
Comparison of picture(Netaji1936.jpg) at different levels applying SPIHT

Result Table (Black and White) STW :
Comparison of picture(Netaji1936.jpg) at different levels applying SPIHT
1 1.319 46.93 78.47 12
2 8.604 38.78 44.79 11
3 31.74 33.12 19.17 9
4 69.98 29.68 8.38 8
5 139.6 26.68 4.02 7
6 292.5 23.47 1.80 6
7 292.5 23.47 1.75 6
8 573.9 20.54 0.73 4

Result Table (Color Image) SPIHT :
Levels MSE PSNR CR Size (KB)
1 4.387 41.71 77.94 9
2 7.445 39.41 26.59 9
3 16.98 35.83 10.98 8
4 38.62 32.26 5.26 8
5 96.5 28.29 2.56 8
6 223.8 24.63 1.16 7
7 449.5 21.6 0.53 5
8 868.6 18.74 0.21 3

Result Table (Color Image) STW :
1 0.9114 48.53 54.34 9
2 3.35 42.88 24.15 9
3 9.983 38.14 12.16 9
4 27.64 33.72 6.44 8
5 76.21 29.31 3.30 8
6 191.5 25.31 1.55 7
7 401.3 22.1 0.69 5
8 806.2 19.07 0.28 3

Conclusion:
At every compression level there is fairly better results are produced
by STW compression techniques. I can conclude that STW is better
compression techniques than the SPIHT.
As compare than gray scale image, compression for true image is
better for all the three parameters. But here too STW have done
better than the SPIHT compression technique.

Future Work :
1. Comparison of this compression technique could be with lifting
scheme compression techniques.
2. SPIHT and STW are called first generation wavelet while lifting
scheme is called second generation wavelet.
3. Second Generation algorithms are called more efficient than first
generation wavelet algorithm. Comparison is available for Wavelet
but comparison for specific technique is needed.

References :
I have used 31 references in my thesis work. There are 7 books, 3 web pages,
21 research paper, I have studied to reach the conclusion.
Some of the references are presented below:
1. Nema, M., Gupta, L., Trivedi, N. R., Video Compression using SPHIT and
SWT wavelet, International Journal of electronics and communication
engineering, ISSN 0974-2166, Vol -5, Nov-2012.
2. Mathworks, www.mathworksin/help/vision/ref/PSNR.html, Last Access
14-Jul-2014, 12:08.
3. Vidaknovic, B., Mueller, P., Wavelet for kids - A tutorial Introduction,
Duke University, AMS subject classification 42A06,41A05,1991.

Questions and Answer ?
Thanking You!

Wavelet, Wavelet Image Compression, STW, SPIHT, MATLAB

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