Hr2615091514

R.Srinivasa Rao, M.Vijay Karthik, Saraswathi Nagla / International Journal of Engineering
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 6, November- December 2012, pp.1509-1514
Wavelet Transform Based Image Compression
R.Srinivasa Rao1, M.Vijay Karthik2,Saraswathi Nagla3
Department of Electronics & Communications Engineering1, Department of Electrical & Electronics
Engineering2,3, Aurora‟s Scientific & Technological Institute, Ranga Reddy Dist, Andhra Pradesh-501301,
INDIA

ABSTRACT
Image require substantial storage and The paper is organized as follows: Integer wavelet
transmission resources, thus image compression Transform described in section II. Section III
is advantages to reduce these requirements. A represents Histogram adjustment for the
good strategy of image compression should preprocessing and post processing of the image
assure a good compromise between a high compression, section IV gives detailed compression
compression rate and a low distortion of the technique, and section V provides the
picture. In this paper a lossless digital image implementation of the proposed technique with
compression technique based on Integer Wavelet results.
Transform is proposed. The small deviations in
data values are not allowed in certain images for II INTEGER WAVELET TRANSFORM
obvious reasons and a potential risk of a person The Wavelet Transform produces floating
misinterpreting an image. A preprocessing and point coefficients even when applied to integer
post processing histogram adjustment is used to values. The original integer data can be
prevent overflow/underflow. In proposed reconstructed perfectly in theory by using these
technique wavelet transform is applied to entire coefficients. However in practice, we usually use
image, so it produces no blocking artifacts. The the fixed point format for data values because the
results show improved high performances in fixed point systems are easier to implement[3] [4].
terms of compression ratio and reconstruction The reduced precession arithmetic used in such
quality. systems can introduce round off errors in the
computations. In practice traditional wavelet
Index Terms; Digital compression, Integer transform have some drawbacks such as it is a
wavelet transform, Histogram modification. floating point algorithm, computer finite word
length will bring in rounding error and signals can‟t
INTRODUCTION be reconstructed exactly, the computation is very
The fast development of computer complicated, computation cost is very high, it
applications came with an enormous increase of the requires more storage space and it is not appropriate
use of digital images, mainly in the domain of to hardware implementation. In order to overcome
multimedia, games, satellite transmissions and above drawbacks, this paper uses lifting scheme
medical imagery. This implies more the research on wavelet - integer wavelet transform[5]. It doesn‟t
effective compression algorithms, the basic idea of depend on Fourier transform, but it still inherits ,
the image compression is to reduce the middle multi resolution properties of traditional wavelet
number of bits by pixel necessary for image transform and transforming coefficient, calculation
representation. The image compression approaches speed is more fast, and it doesn‟t need extra storage
can be divided in two methods: lossless and loss. cost so it is called second generation wavelet
Different compression approaches have been studied transform. Hence in applications where we need
in the literature[1]. lossless reconstruction, we need transforms which
A lossless high-capacity data for have reversibility properties even when reduced
image compression based on integer wavelet is precision is used. It was shown by calderbank et al.,
proposed. After extracting data embedded, the that we can build wavelet transforms that map
original image should be reversible from compressed integers to integers by using lifting structure. The
image[2]. The wavelets are excellent approximates reversibility property is obtained by rounding of the
and signal analyzers. Their time-frequency analysis predict filter or update filter output before adding or
makes them an effective and innovative tool. subtracting in each lifting step. Wavelet filters are
In this paper, we investigate integer decomposed into basic modules by integer wavelet
wavelet transform technique for transforming the transform, that is, wavelet transform is completed
image. The basic idea behind this technique is to through splitting, predicting and updating, as figure
use integer wavelet to transform the data into the 1 displays.
different basis. A pre and post histogram is used for
A preprocessing and post processing histogram
adjustment is used to prevent overflow/underflow.

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+ J i-1 -
0.018

0.016

0.014
SPLIT
P U U P MERGE Ji 0.012
Ji

Density
0.01

0.008

0.006

K i-1 0.004
- + 0.002

0
50 100 150 200 250
Fig 1. Integer wavelets transform decomposition and Data

Reconstruction diagram Fig 2(b). Gray scale histogram modification
modified histogram
After integer wavelet transform, it has four
sub-bands. We will embed the information into
three high frequency sub bands. Except that it has 0.018

advantages of traditional wavelet transform, integer 0.016

wavelet transform which is applied to digital 0.014

compression technology has following 0.012

advantages[6]:
Density

0.01
(1) It avoids rounding error of floating point in 0.008
mathematical transformation; 0.006
(2) Its transforming speed is fast and it doesn‟t
0.004
need extra storage cost.
0.002

0
III HISTOGRAM ADJUSTMENT 40 60 80 100 120 140
Data
160 180 200 220 240

For a given image, after data embedding in
some IWT coefficients, it is possible to cause Fig 2(c). Gray scale histogram modification
overflow/underflow, which means that after inverse histogram after data embedding.
wavelet transform the gray scale values of some
pixels in the compressed image may exceed the IV PROPOSED COMPRESSION SCHEME
upper bound (255 for an eight-bit grayscale image) 1. Data Embedding Process:
and/or the lower bound (0 for an eight-bit grayscale The main steps of the embedding procedure
image). In order to prevent the overflow/underflow, developed are presented here and summarized.
we adopt histogram modification, which narrows a. Histogram modification is applied on
the histogram from both sides as shown in. Fig.2. original image that prevents possible
Please refer to [7],[8] for the detailed algorithm. overflow and underflow.
The bookkeeping information will be embedded b. We first apply integer wavelet
into the cover media together with the information decomposition to the original image. In our
data. experiments, CDF (2, 2) wavelet filters are
used to decompose the original gray scale
image into one level. After integer wavelet
0.018 transform, it has four sub-bands.
0.016 c. In order to have the compressed image
0.014 perceptually the same as the original image,
0.012 we choose to hide data in one (or more than
one) “middle” bit-plane(s) in the IDWT
Density

0.01

0.008 domain. To further enhance the visual
0.006
quality of the compressed image, we embed
0.004
data only in the middle and high frequency
0.002
sub bands, specifically in the LH1, HL1 and
0
40 60 80 100 120 140 160 180 200 220 HH1 sub bands.
Data
d. Construct binary images from 5th bit of
Fig 2(a). Gray scale histogram modification of
LH1, HL1 and HH1 wavelet coefficients.
Original histogram
For constructing binary image using LH1,
the each integer wavelet coefficients in
LH1 is converted into 8 bit binary
sequence, if 5th bit of each binary sequence

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is 1 then assign 2 to binary image otherwise 2. Extraction Process
assign 1. For constructing binary image Extraction of compressed image and inverting of
using HL1 and HH1 is same as above. compressed image into original one is reverse
e. Compress data in binary image obtained process of embedding.
from LH1, HL1 and HH1 by using
arithmetic coding because of its high a. Perform histogram modification on
coding efficiency. compressed image.
f. Insert the header information and b. Perform one level integer wavelet
compressed data together, the embed signal decomposition on compressed image.
consists of these three. If embedded bit is c. Extract the embed signal from 5th bit of
1or (0) then convert first integer wavelet LH1, HL1 and HH1 wavelet coefficients.
coefficient in LH1 sub band into 8 bit
binary sequence and replace 1or (0) to the For extracting embed signal with using LH1, the
5th bit plane of that binary sequence and each integer wavelet coefficient in LH1 is converted
convert back to integer. In this way all the into 8 bit binary sequence and if 5th bit of each
embedded bits hide in “5th” bit-plane in the binary sequence is 1, then embed bit is 1 otherwise
LH1, HL1 and HH1 coefficients. embed bit is 0.
g. The way of accessing each wavelet The sample code given below:
coefficient for embedding depends on
secret key. Index=1
h. A secret key function that keeps the hidden for i=1: size (LH1, 1)
data secret even after the algorithm is for j=1:size(LH1,2)
known to public. binSeq = dec2bin (abs (LH1(i, j)),8);
i. Take the Inverse integer wavelet transform if binSeq (5) == '1'
to reconstruct the compressed image. embed Signal (index, 1) = 1;
j. Perform histogram modification on else
compressed image. embed Signal(index,1) = 0;
k. The invisibility of the compressed image. end
We use the formula (1) to compare the difference index = index + 1;
between the original image and the compressed end
image, Figure 5 demonstrates that the compressed end
image embedded with the proposed algorithm is
invisible, where (a) is the original image, and (b) For extracting embedded signal with using HL1
is the compressed image with compression ratio and HH1 same as above.
=91.25. (a) Based on header information extract
binary compressed image from embed
٢ = (1- Tc / To) X 100 (1) signal.
(b) Extract the respective binary images of
Where Tc Is Size of Original cover image LH1, HL1 and HH1 from embed signal
To Is Size of Compressed cover image based on header information.
(c) Decompress to get the original
sequence.
(d) Insert the uncompressed 5th bit data
back into LH1, HL1 and HH1.
(e) Take the Inverse integer wavelet
transform to reconstruct the original
image.
(f) Perform histogram adjustment on original
image.

Fig.3 Embedding Method

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(a) (b)

Fig.4 Extraction method

V IMPLEMENTATION
The program code is written in (c) (d)
„MATLAB‟. Test images of „Airplane‟, „Lena‟, Fig.6 Compressed images (a) Compressed
„Baboon‟, „Gold hill‟, and „Barbara‟ are used as Goldhill image (b) Compressed Baboon image (c)
input images for validation of developed Compressed Barbara image (d) Compressed Lena
algorithms. The wavelet decomposition of image image
is done by using CDF (2,2) wavelet filter.
The compressed logo is binary image created and Table I The Compression Ratio(%)
embedded as per algorithm discussed. The Value
embedding is done for the visible compressed
logo. The resultant coefficients were inverse Host Compression
transformed to obtain the compressed image. Image Ratio value(%)
Several test gray scale images of size 512×512 are 512×512
used in experiments. The original and compressed Lena 81.36
Airplane images are shown in fig.5. Compression
Baboon 89.13
ratio value of Airplane image after compressed
embedding is measured as 91.25%. It is observed Goldhill 78.57
that imperceptibility requirement is met. The Airplane 79.23
same experiment is conducted on other four Barbara 84.56
images. Fig.6 contains other four compressed
images. Table I shows some experimental results.
Table I show that Airplane image has a better
embedding capacity than the other images in the
experiment. It also shows it has a better visual
quality as far as peak signal to noise ratio is
concerned.
Table II shows image quality tested for different
payloads on the same image using different
wavelets. Among various wavelet filters,
CDF(2,2) performs better than others for the same
payloads. Image quality quickly changes when
different wavelets are used.
2

(a) (b) PSNR  255
M N

 (H (i, j) W (i, j))
1 2

Fig.5 Airplane image : (a) Original Airplane M N i 1 j 1
(2)
image
(b) Compressed image (91.25%) Where H (i, j) Is Original cover image
W (i, j) Is Compressed image

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Table II Comparison of performance of
various wavelet families on Airplane image for 250000
different payload size 196152
200000
Payloa cdf(2,2) db2 Sym4 bior3.3 bior6.8 rbio3.3
150000
d PSNR PSNR PSNR PSNR PSNR PSNR
bits (db) (db) (db) (db) (db) (db) 94000
Number of Bits
100000
10000 37.78 35.84 36.37 36.31 36.31 36.24
15129 37.73 35.78 36.25 36.28 36.23 36.29 50000 24000
20164 37.67 35.73 36.26 36.24 36.26 36.16
25281 37.60 35.69 36.11 36.16 36.00 35.99 0
50176 37.11 35.708 35.89 35.76 35.85 35.58 Goljan,s Gurong Proposed
75076 36.84 35.67 35.90 35.71 36.00 34.67
10048936.74 ** 35.86 35.51 35.05 33.86
Fig.8 Comparison between proposed and
existing methods
Image Quality Tested on different wavelets
38
CONCLUSION
37.5 Simulation experiments on the digital
compression of images have been performed using
Image Quality (PSNR db)

37
two standard images: Lena and Airplane. In
36.5 proposed method we verify the compromise that
exists between the compression ratio and the quality
36
of the rebuilt image. The proposed image
35.5
compression algorithm based on integer wavelet
transform is able to embed up to 81.36% and
35 cdf2.2 91.25% compression ratio value and into image of
db2
Sym4 512 by 512 imperceptibly and extracts the embedded
34.5
bior3.3 data and original image from compressed image
34
bior6.8 without loss of information. The performance of
rbio3.3
proposed lossless compression algorithm verified by
33.5 various wavelet filters. Among various wavelet
1 2 3 4 5 6 7 8 9 10
Payload Bits 4
x 10 filters, CDF (2,2) performs better than others for the
same payloads.
Fig.7 Image Quality Tested on Different Wavelets
REFERENCES
Table III shows the comparison between existing [1] W. Sweden‟s, “The lifting scheme: A
methods in literature and proposed method. The custom-design construction of biorthogonal
proposed method is able to embed up to 196k bits wavelets,” Appl. Comput. Harmon. Anal.,
into image of 512 by 512 imperceptibly. vol. 3, no. 2, pp. 186–200, 1996.
[2] Fridrich, J.,Goljan, M., Du, R., "Invertible
Table III Comparison between existing methods Authentication", In: Proc. SPIE, Security
and proposed method and Compression of Multimedia Contents,
San Jose, California January 2001
Methods The amount of data [3] Jiang Zhu. M., Guorong Xuan., Jidong
embedded in a 512 × Chen., "Distortion less data hiding based on
512 image integer wavelet transform ", Vol.38, No.25,
Electronics Letters 5th December 2002.
Goljan‟s 3,000-24,000 bits [4] I. Daubechies and W. Sweldens,
Guorong 15,000-94,000 bits “Factoring wavelet Transforms into lifting
steps,” J. Fourier Anal. Appl.,vol. 4, no. 3,
Proposed 10000-1,96152 bits pp. 245–267, 1998.
[5] M. D. Adams and F. Kossentini,
“Performance evaluation of reversible
integer-to-integer wavelet transforms for
image compression,” in IEEE Data
Compression Conference, now bird, UT,
USA, March 1999, pp. 514–524, IEEE.

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[6] A. R. Calderbank, I. Daubechies, W.
Sweldens and B. Yeo, “Wavelet transforms
that map integers to integers,” Applied and
Computational Harmonic Analysis, vol.5,
no.3, pp.332-369, 1998.
[7] G. Xuan, C. Yang, Y. Q. Shi and Z. Ni:
High Capacity Lossless Data Hiding Saraswathi Nagla was born in Nizamabad, India in
Algorithms. IEEE International Symposium 1986. At present she is working as Assistant
on Circuits and Systems (ISCAS04), Professor in the Department of Electrical &
Vancouver, Canada, May 2004. Electronics Engineering, Aurora‟s Scientific and
[8] D. Kundur, D.Hatzinakos, "Digital Technological Institute, Ranga Reddy Dist -501301,
compression using multi resolution wavelet Andhra Pradesh, India. She obtained her M.E
decomposition", Proceedings of the IEEE Degree from Chaitanya Bharathhi Institute of
international conference on acoustics, Technology (CBIT) Gandipet, Osmania University,
speech and signal processing, Seattle, 1998. Hyderabad, and Andhra Pradesh, India. She
Obtained B-Tech Degree from Srinivasa Reddy
Institute of Technology, Munipally, JNTU
R. Srinivasa Rao was born in Hyderabad, Andhra Pradesh. Her research area
West Godavari, India in 1977. includes Image Processing, Wavelets, Power
At present he is working as Quality, Power System, and Power Semiconductor
Associate Professor in the Drives.
Department of Electronics and
Communications Engineering,
Aurora‟s Scientific and Technological Institute,
Ranga Reddy Dist -501301, Andhra Pradesh, India.
He obtained his M.Tech degree JNTU College of
Engineering, JNTU Hyderabad, and Andhra
Pradesh, India. He completed Graduation in
Engineering, AMIE, The Institution of Engineers
(INDIA), Kolkata. His research area includes
Signals and Systems, Digital Image Processing and
communication systems.

Mamidala Vijay Karthik was born in
Hyderabad, India in 1985. At present he is working
as Senior Assistant Professor in the Department of
Electrical & Electronics Engineering, Aurora‟s
Scientific and Technological Institute, Ranga Reddy
Dist -501301, Andhra Pradesh, India. He obtained
his M.E degree from Chaitanya Bharathi Institute of
Technology (CBIT) Gandipet, Osmania University,
Hyderabad, and Andhra Pradesh, India. He obtained
B.Tech degree from Church Institute of Technology,
Gagillapur, JNTU Hyderabad, and Andhra Pradesh.
His research area includes Wavelets, Power Quality,
Power System, and Power Semiconductor Drives.

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Hr2615091514

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