Analysis of image compression algorithms using wavelet transform with gui in matlab

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 02 Issue: 10 | Oct-2013, Available @ http://www.ijret.org 595
ANALYSIS OF IMAGE COMPRESSION ALGORITHMS USING
WAVELET TRANSFORM WITH GUI IN MATLAB
Y.Sukanya1
, J.Preethi2
1
Associate professor, 2
M-Tech, ECE, Vignan’s Institute Of Information Technology, Andhra Pradesh ,India
Sukanya_ece@rediffmail.com, Preetupriti@gmail.com
Abstract
Image compression is nothing but reducing the amount of data required to represent an image. To compress an image efficiently we
use various techniques to decrease the space and to increase the efficiency of transfer of the images over network for better access.
This paper explains about compression methods such as JPEG 2000, EZW, SPIHT (Set Partition in Hierarchical Trees) and HS-
SPIHT on the basis of processing time, error comparison, mean square error, peak signal to noise ratio and compression ratio. Due
to the large requirement for memory and the high complexity of computation, JPEG2000 cannot be used in many conditions especially
in the memory constraint case. SPIHT gives better simplicity and better compression compared to the other techniques. But to scale
the image more so as to get better compression we are using the line-based Wavelet transform because it requires lower memory
without affecting the result of Wavelet transform. We proposed a highly scalable image compression scheme based on the Set
Partitioning in Hierarchical Trees (SPIHT) algorithm. This algorithm is called Highly Scalable SPIHT (HS_SPIHT) it gives good
scalability and provides 1 bit stream that can be easily adapted to give bandwidth and resolution requirements.
Keywords: - Wavelet transform Scalability, SPIHT, HS-SPIHT, Processing time, Line-based Wavelet transform.
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1. INTRODUCTION
Compression is the process of reducing large data files into
smaller files for efficiency of storage and transmission.
Data compression techniques are:
a. Lossless data compression
b. Lossy data compression
Lossless data compression is nothing but the original data can
be reconstructed exactly from compressed data.
Lossy data compression in which data after compression and
then decompression retrieves a file that is not exactly as the
original data as there will be loss of data.
1.1. Wavelets Definition
Wavelets are mathematical functions that cut up data into
different frequency components. The fundamental idea behind
wavelets is to analyze the signal at different scales or
resolutions, which is called multiresolution.
1.2. Wavelet Transform
The most important feature of wavelet transform is it allows
multiresolution decomposition. An image that is decomposed
by wavelet transform can be reconstructed with desired
resolution. The procedure for this is a low pass filter and a
high pass filter is chosen, such that they exactly halve the
frequency range between themselves. This filter pair is called
the Analysis Filter pair. First of all, the low pass filter is
applied for each row of data, and then we obtain low
frequency components of the row. As the LPF is a half band
filter, the output data consists of frequencies only in the first
half of the original frequency range. By Shannon's Sampling
Theorem, they can be sub sampled by two, so that the output
data contains only half the original number of samples,
similarly the high pass filter is applied for the same row of
data, and now the high pass components are separated, and
placed by the side of the low pass components. This procedure
is done for all rows.
LL HL
LH HH
Ist level
LL HL HL
LH HH
LH HH
2nd level

__________________________________________________________________________________________
LL HL HL
HLLH HH
LH HH
LH HH
3rd level
Fig -1: wavelet decomposition.
Next, the filtering is done on each column. as a result we get
four bands of data, each labeled as LL (low-low), HL (high-
low), LH (low-high) and HH (high-high).The LL band can be
decomposed once again in the same manner, thereby
producing even more sub bands[4]. This can be done up to any
level, thereby resulting in a pyramidal decomposition as
shown above the LL band at the highest level can be said as
most important, and the other bands are of lesser importance,
the degree of importance decreases from the top of the
pyramid to bottom.
2. APPROACH
Fig -2: Block diagram for image compression
One of the most important characteristics of DWT is
multiresolution decomposition. An image is considered and
forward wavelet transforms applied on the image then the
image is decomposed the decomposed image is given to the
quantizer. The quantizer approximates the continuous set of
values in image data with finite set of values. after that data
can be encoded using entropy coder to give additional
compression. Next is the decoder that carries decoding process
i.e. reading the unique code bits sent in place of data bits. the
dequantizer dequantizes the decoded data bits then finally the
inverse transformation is the process of retrieving back the
image data from the obtained image values.
3. IMAGE COMPRESSION ALGORITHMS
JPEG 2000
EZW
SPIHT
HS-SPIHT
4. JPEG-2000 IMAGE CODING
JPEG 2000 is the international standard for still images. This
is the enhancement to the existing JPEG system. The JPEG
2000 implements a new way of compressing images based on
the wavelet transform. This supports lossy and lossless
compression of grayscale as well as color images. Here we
have 2 processes encoding and decoding process.
4.1. Encoding Process
Image
Output
Fig -3: Encoding block diagram of JPEG 2000 algorithm
The input image is given to preprocessor, in this step tiling is
done .tiling is nothing but dividing the image into rectangular
and non-overlapping tiles of equal size and then each tile is
compressed independently using its own set of specified
compression parameters. The preprocessed image is given to
DWT here wavelet decomposition is done the output of DWT
is given to uniform quantizer which reduces precision of sub
band coefficients so that fewer bits will be needed to encode
transformed coefficients. then output of quantizer is given to
embedded block coding which uses wavelet transform to
generate the sub band this sub band is partitioned into small
blocks of samples called code blocks EBCOT generates a
separate highly scalable bit stream for each code block, next is
the rate control block which adjusts the quantizer step size or
discards some coding pass information
4.2. Decoding Process
Compressed data
Reconstructed image
Fig -4: Decoding block diagram of jpeg 2000
Image Forward
Wavelet
transform
mm
quantizer Encoder
Retrieved
image
Inverse
wavelet
transfor
m
dequa
ntizer
Decod
er
preproc
essing
DWT
Uniform
quantizer
Bit stream
organization
Rate
control
Embedde
d block
coding
Compr
essed
data
Inverse
DWT
Inverse
ICT
Dequa
ntizatio
n

__________________________________________________________________________________________
decoder perform opposite to encoder ,The output of encoder
i.e. the code stream is received by the decoder .the coefficients
in packets are decoded ,then dequantized and reverse ICT is
performed to get reconstructed image.
Important point of jpeg 2000 is here compression can be done
in one way but decompression is done in many ways.
5. EMBEDDED ZERO TREE WAVELET CODING
EZW stands for embedded zero tree wavelet An EZW encoder
is specially designed to use with wavelet transforms. The is
based on progressive coding to compress an image into bit
stream with increasing accuracy so when more bits are added
to a bit stream image will be more detailed.
Fig -5: Block diagram of Embedded zero tree wavelet coding
5.1 Approach
Before the processing of image data the image is preprocessed
.In preprocessing step tiling on the original image is done. All
operations, including component mixing, wavelet transform,
quantization and entropy coding are performed independently
on the image tiles. Tiling reduces memory requirements, and
as they are also reconstructed independently, they can be used
for decoding specific parts of the image instead of the whole
image. All tiles have exactly the same dimensions, except
some of those at the boundary of the image. This unit
transforms the input image from time domain to frequency
domain and decomposes the original image into its
fundamental components.
The wavelet transform uses filter banks for the decomposition
of preprocessed image. The Embedded ZeroTreeWavelet
(EZW) encoder encodes the decomposed image by
recognizing the priority of decomposed image pixel. The
encoder module calculates a initial threshold for coding given
by T0= 2(log
2
c
max
)
.
The encoding process is performed using 2 passes namely
1. dominant pass and
2. Subordinate pass.
The dominant pass generates any one of four possible
combinations like they are significant positive(SP),
significant negative (SN), isolated zero(IZ) and zerotree
root(ZR).
Subordinate pass where the coefficients are encoded as 0 or 1
depending on the current threshold.
The decoding unit reconstructs the values by identifying the
symbols as positive, negative, zero tree and isolated zero tree.
Inverse transformation is the process of retrieving back the
image data from the obtained image values. The image data
transformed and decomposed under encoding side is
rearranged from higher level decomposition to lower level
with the highest decomposed level been arranged at the top.
Fig 5 shows the reconstruction of the obtained decomposed
component.
5.2 The Algorithm
1. Set the initial threshold T0= 2(log
2
c
max
)
.here xmax is the
maximum coefficient value.
2. set k=0
3. Conduct dominant pass by scanning the data Outputs will
be any of 4 conditions below i.e.
a. If value of coefficient is greater than the threshold
and the value is positive, it means the output
significant positive.
b. If value of coefficient is greater than the threshold
and the value is negative, it means the output
significant negative.
c. If magnitude of coefficient is less than the threshold
and all its descendants have magnitudes less than the
threshold then coefficient is labeled as zero tree roots.
d. If magnitude of coefficient is less than the threshold
and all its descendants have values greater than the
threshold then coefficient is labeled as isolated zero
4. Conduct a subordinate pass or refinement pass by scanning
through the data to refine the pixels already known to be
significant in current bit plane.
5. Set k=k+1 and the threshold Tk=Tk-1/2.
6. Stop if the stopping criterion is met or go to step 3.
6. SPIHT ALGORITHM
Set Partioning in Hierarchical Trees (SPIHT) is a wavelet
based image compression method.
SPIHT introduces three lists:
a. List of Significant Pixels (LSP),
b. List of Insignificant Pixels (LIP) and
c. List of Insignificant Sets (LIS).
First initialization is done, and then algorithm takes two stages
for each level of threshold

__________________________________________________________________________________________
1. The sorting pass (in which lists are organized) and
2. The refinement pass.
LIS is further divided into two types of sets of insignificant
pixels .They are
Type A (all descendant are zero)
Type B (all grandchildren and further descendants are zero).
SPIHT algorithm defines four types of sets, which are sets of
coordinates of coefficients:
O(i,j): set of coordinates of all offspring of node (i,j); children
only
D (i,j): set of coordinates of all descendants of node (i,j);
children, grandchildren, great-grand, etc.
H (i,j): set of all tree roots (nodes in the highest pyramid
level); parents
L (i,j): D (i,j) – O(i,j) (all descendants except the offspring);
grandchildren, great-grand, etc.
Fig -6: Block diagram of SPIHT
To find the number of passes we use the formula
n =[ log
2
c
max].
We find initial threshold as T0=2n
.
The SPIHT algorithm forms a hierarchical quad tree data
structure for the wavelet transformed coefficients. The set of
root node and corresponding descendants are together called
as spatial orientation tree (SOT).
Fig -7: Quad tree structure
7. LINE- BASED WAVELET TRANSFORM:
In general in wavelet transform all the lines are horizontally
filtered before vertical filtering and thus the total image data
should be stored. But the line-based wavelet transform starts
vertical filtering as soon as a sufficient number of lines,
determined by the filter length have been horizontally filtered.
This algorithm requires storing a minimum number of lines.
The image data are stored in memory only while they are used
to generate output coefficients, and removed from memory
immediately once no longer being needed, therefore the
memory requirements are greatly reduced.
8. HS_SPIHT ALGORITHM
The HS_SPIHT algorithm proposed here solves the spatial
scalability problem by introducing of resolution-dependent
sorting pass that uses one additional list, called the list of
delayed insignificant sets (LDIS). The HS_SPIHT coder first
encodes all bit planes for a given (low) resolution level and
then moves to the next higher resolution level
Sets encountered during the sorting pass that lie outside the
actually considered spatial resolution are temporarily stored in
the LDIS. They are moved back from the LDIS into the LIS
when they are required for encoding the next higher
resolution. According to the magnitude of the coefficients in
the wavelet pyramid, coding of higher resolution bands
usually starts from lower bit planes. Therefore, during the
encoding process of resolution level k, the encoder keeps the
number of coefficients that went to the LDIS for each
quantization level.
After finishing the encoding process for all bit places of
resolution level k, the encoder knows which entries in the
LDIS that belong to which bit plane. To encode the additional
three sub bands for resolution level k-1, it moves the related
entries of the LDIS that belong to the actual bit plane to the
LIS and carries out the sorting of LIS with the same procedure
as before.
Altogether, the total number of bits belonging to a particular
bit plane is the same for SPIHT and HS_SPIHT, but
HS_SPIHT distributes them differently among the different
spatial resolution levels.
8.1The Algorithm
The HS-SPIHT algorithm also uses three lists they are
1. LIP
2. LSP
3. LIS
Algorithm consists of both encoding and decoding process.
Encoding:
Step 1: initialization.
Original
image
Wavelet
transform
Sorting
pass
Transmission Entropy
coding
Refinem
ent pass

__________________________________________________________________________________________
Choose threshold T0=2[log
2
c
max]
Step 2:load the LIP with {(0,0),(0,1),(1,0),(1,1)}
Step 3:load LIS with descendants i.e. {D(0,1),D(1,0),D(1,1)}.
Step 4: LSP=Empty.
Step 5: Process LIP
If (0,0)>T0,we transmit 1 and load LSP with(0,0);if
(0,0)>0 we transmit 0.
Step 6: Process LIS if
D(0,1),D(1,0),D(1,1)<T0 transmit 0.
We get a bit stream
Decoding:
Step 1: Initialization
n=[ log
2
c
max ]
Step 2: Find threshold T0=2n
.
Step 3: consider LIP, LSP, LIS
Step 4: consider the encoded bit steam
Step 5: Process LIP
Receive the bit stream, if 1st bit is 1 combine next bit to 1
i.e.10 this indicates ist element of LIP is significant positive.
If next bit is 0 we it as insignificant
Step 6: reconstruct the 1st element of LIP value by( 3/2)*2n
.
Step 6: if D(0,1),D(1,0),D(1,1)<T0 we get 0
Step 7: Finally again load LIP, LSP, LIS.
9. RESULTS
For Camera Man Image
METHOD INPUT IMAGE OUTPUT IMAGE
EZW
JPEG 2000
SPIHT 1ST
LEVEL
2ND
LEVEL

__________________________________________________________________________________________
3RD
LEVEL
HS-SPIHT 1ST
LEVEL
2ND
LEVEL
3RD
LEVEL
Table:
METHOD MEMORY
IN MB
SIZE MSE PSNR PROCESSING
TIME
COMPRESION
RATIO
EZW 3.064 1*290493 0.23 30.4481 1.9 4.44
JPEG
2000
1.859 1*204930 0.26 29.9157 1.12 4.46
SPIHT
1st
level
3.4 1*425988
0.23 30.4481 40.6
12.595
2nd
level
3.61 1*451808 13.2009
3rd
level
3.84 1*480133 13.4692
HS-
SPIHT
1stlevel 3.818 1*439871
0.68 29.76 39.45
13.9535
2nd
level
3.648 1*456117 16.9535
3rd
level
3.875 1*484442 16.2625

__________________________________________________________________________________________
For Medical Image:
METHOD INPUT IMAGE OUTPUT IMAGE
EZW
JPEG 2000
SPIHT 1ST
LEVEL
2ND
LEVEL
3RD
LEVEL
HS-SPIHT 1ST
LEVEL
2ND
LEVEL

__________________________________________________________________________________________
3RD
LEVEL
Table
METHOD SIZE MEMORY
IN MB
MSE PSNR PROCESSING
TIME
COMPRESSION
RATIO
EZW 1*198828 1.5 0.23 30.448 3 4.43
JPEG
2000
I*202692 1.62 0.54 26.74 138.67 8.66
SPIHT 1st
level
1*384046 0.27 0.13 56.958 38.796 15.3782
2nd
level
1*408208 0.261 16.0181
3rd
level
1*436167 0.257 16.2924
HS-
-SPIHT
1st
level
1*428931 0.40 1.15 23.4547 50.391 10.3561
2nd
level
1*404991 0.24 10.3540
3rd
level
1*482417 0.227 18.4595
CONCLUSIONS
 In this paper Image is considered and wavelet
transform is applied on the image and wavelet
decomposition is done.
 Four algorithms in terms memory spacing, size,
compression ratio, mean square error, peak signal to
noise ratio are analyzed.
 We proposed HS-SPIHT algorithm which gives us
better scalability and reduced bit stream i.e. size of
image is reduced well and it also gives better
compression ratio .
 So this paper presents comparative analysis between
compression algorithms. In this work we have
provided the basics of wavelet transform and
comparisons of different algorithms used for an
image.
 Finally we get reduced bit stream and better
scalability.
REFRENCES
[1]. Puja D Saraf, Deepti Sisodia, Amit Sinhal and Neetesh
Gupta , “Comparisons of wavelets based image compression
methods”,World Journal of Science and Technology 2012,
2(3):10-13 ISSN: 2231 – 2587.
[2]. D.Vijendra babu , Dr.N.R.Alamelu “Wavelet Based
Medical Image Compression Using ROI EZW” ,International
Journal of Recent Trends in Engineering, Vol 1, No. 3, May
2009.
[3].K.Sivanagireddy,M.Saipravallika,P.K.Chandrika
Tejaswini, “Low memory low complexity image compression
using DWT and HS-SPIHT encoder ”,International Journal of
Scientific & Engineering Research Volume 3, Issue 8, August-
2012.
[4]. Ruchika, Mooninder Singh, Anant Raj Singh
“Compression of Medical Images Using Wavelet Transforms”
, International Journal of Soft Computing and Engineering
(IJSCE) ISSN: 2231-2307, Volume-2, Issue-2, May 2012.
[5] .Peng Jiang, Qingbo Huang, Yaguang Kang and Li Chai,
“Research on Compression Method based on IWT and SPIHT
for Historical Data in Process Industry”, Computer and
Computational Sciences 2006, Proceedings (IMSCCS’06).
[6] . J.M. Shapiro, “Embedded image coding using the zero
trees of wavelet coefficients”, IEEE Transactions on
ImageProcessing, Vol. 41, No. 12, pp. 3445-3462, December
1993.
[7]. Yen-Yu Chen*, “ Medical image compression using
DCT-based subband decomposition and modified SPIHT data
organization”, international journal of medical informatics 7 6
( 2 0 0 7 ) 717–725Department of InformationManagement,

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ChengChou Institute of Technology, 6, Line 2, Sec 3,Shan-
Chiao Rd., Yuanlin, Changhwa, Taiwan.
[8]. W. Pennebaker and J. Mitchell, JPEG Still Image Data
Compression Standard. Van Nostrand Reinhold, 1994.
[9]. Subramanya A, “Image Compression
Technique,”Potentials IEEE, Vol. 20, Issue 1, pp 19-23, Feb-
March2001,
[10]. David Jeff Jackson & Sidney Joel Hannah,
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Southeastern Symposium,pp 513-517, 7 –9 March 1993.
BIOGRAPHIES
Mrs. Y. Sukanya received her B. Tech Degree
in ECE Department from S.R.K.R Engineering
College, Bheemavaram and obtained her
M.Tech degree in Digital Electronics and
Communication Systems from Gudlavalleru
Engineering College. She has eight years of teaching
experience, currently working at Vignan's Institute of
Information Technology, Visakhapatnam as Associate
Professor in Department of ECE. Her Area of interests are
Communication systems and signal processing.
Ms. J.Preethi has obtained B.Tech degree
from Vignan’s institute of information
technology affiliated to JNTUK in the year
2011. Now she is pursuing M.Tech Degree in
Department of Electronics & Communications,
Vignan's institute of Information and Technology,
Visakhapatnam. She is interested in the fields of image
processing.

Analysis of image compression algorithms using wavelet transform with gui in matlab

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