A systematic image compression in the combination of linear vector quantisation and discrete wavelet transform

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 03 Issue: 04 | Apr-2014, Available @ http://www.ijret.org 248
A SYSTEMATIC IMAGE COMPRESSION IN THE COMBINATION OF
LINEAR VECTOR QUANTISATION AND DISCRETE WAVELET
TRANSFORM
K. Kalaivani1
, C. Thirumaraiselvi2
1
PG Student, Sri Krishna College of Engg & Tech, Coimbatore
2
Associate Professor, Sri Krishna College of Engg & Tech, Coimbatore
Abstract
As the use of digital image is increasing day by day, and the amount of data required for an acceptable quality image is high, there
begins a high necessity for image compression. Vector quantisation (VQ) is a novel technique for image compression. VQ is a lossy
compression scheme, used to compress image both in spatial domain & frequency domain. One of the major disadvantages is high
encoding time & complexity. In spite of these disadvantages it is highly preferred due to its advantages like high reconstruction
quality at low coding rates and rapid decoding. Thus in order to reduce the high encoding time we go for the use of neural network.
There are various types of neural networks are available. The proposed algorithm uses the most effective and simple methods like self
organizing maps and linear vector quantization together with the discrete wavelet transform in order to reduce the loss of information
during compression and their results are compared.
Keywords- Image compression, Neural network, Self organising maps, Linear vector quantization, discrete wavelet
transform.
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1. INTRODUCTION
A Common characteristic of most images is that the
neighbouring pixels are correlated and therefore contain
redundant information. The foremost task then is to find less
correlated representation of the Image. Two fundamental
components of compression are redundancy and irrelevancy
reduction. Redundancy reduction aims at removing
duplication from the signal source (image/video).Irrelevancy
reduction omits parts of the signal that will not be noticed by
the signal receiver namely Human Visual System(HVS).In
general three types of redundancy can be identified as
(i)Spatial Redundancy, (ii)Spectral redundancy, (iii)
Temporal redundancy .
Image compression research aims at reducing the number of
bits needed to represent an image by removing the spatial and
spectral redundancies as much as possible. In many different
fields, digitized images are replacing conventional analog
images as photograph or x-rays. The volume of data required
to describe such images greatly slow transmission and makes
storage prohibitively costly. The information contained in
images must, therefore, be compressed by extracting only
visible elements, which are then encoded. The quantity of data
involved is thus reduced substantially. The fundamental goal
of image compression is to reduce the bit rate for transmission
or storage while maintaining an acceptable fidelity or image
quality.
One of the most successful applications of wavelet methods is
transform-based image compression. A Discrete wavelets
transform is the combination of the low pass and high pass
filtering in a spectral decomposition of signals along with a
very fast implementation. There are various reasons for
choosing discrete wavelets transforms. They have extremely
fast implementation, weighting factor. Their reciprocal can be
implemented using only integer addition and bit shifts, which
are extremely fast operation. The overlapping nature of the
wavelet transform alleviates blocking artifacts, while the
multiresolution character of the wavelet decomposition leads
to superior energy compaction and perceptual quality of the
decompressed image. Furthermore, the multiresolution
transform domain means that wavelet compression methods
degrade much more gracefully than block-DCT methods as the
compression ratio increases. Wavelet-based coding [1]
provides substantial improvements in picture quality at higher
compression ratios.
Vector quantization is one of the commonly used techniques
for data compression. A vector quantizer maps k-dimensional
vectors in the vector space Rk [2] into a finite set of vectors Y
= {Yi: i = 1, 2... N} each vector Yi is called a code vector or a
code word, and the set of all the code words is called a

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codebook. The wavelet coefficients obtained at the wavelet
decomposition level are converted into blocks. Then by
applying vector quantization technique the blocks are
converted into VQ code vectors. In the encoding stage, the VQ
code vectors are compared with every SOFM code vectors in
the initial codebook using Euclidean distance formula.
Euclidean distance is computed as follows:
The VQ code vectors found to be the closest in distance given
by Eq.(1) from the input vector to the vector block is declared
as the winning VQ code vectors. The indices of the winning
VQ code. Vectors will be stored. These indices will be passed
through a channel to the decoder.
Self–Organizing Map based neural network technique is used
for initial codebook generation. SOM is a clustering technique
having several desirable features and consequently it has
attracted the attention of researchers in the field of vector
quantization [3] [4]. The learning scheme of self-organizing
map is based on Least Mean Square (LMS) [5] algorithm. In
LMS algorithm the weights of the neurons are modified „On
the fly‟ for each input vector. SOM will generate more code
vectors for the high density region.
Kohonen's learning vector quantization algorithm (LVQ) is a
supervised variant of the self-organizing map algorithm
(SOM) that can be used for labelled input data. Both SOM and
LVQ are based on neurons representing prototype vectors and
use a nearest neighbour approach for clustering and classifying
data. So, they are neural network approaches particularly
useful for non-linear separation problems. In LVQ labels
associated with input data are used for training. The learning
process tends to perform the vector quantization starting with
the definition of decision regions and repeatedly reposting the
boundary to improve the quality of the classifier.
2. EXISTING METHODOLOGIES
Shapiro [6] first introduced the notation of embedded coding
called as Embedded Zero tree Wavelet coding (EZW) which
yields output of low psycho visual quality image. Lewis and
Knowles [7] constructed a wavelet function which uses the
piecewise constant function. The wavelet function used by
Lewis failed to produce image without blocking effects.
Daubechies [2] introduced a family of compactly supported
orthogonal wavelet systems with fixed regularity. The wavelet
method proposed by Daubechies yields output with PSNR
value ranges from 22 dB to 36 dB for various wavelet
coefficients. Mallat [8] proposed the theory of multi resolution
wavelet analysis known as Mallat algorithm which reduces the
dimensionality with higher computational load. Pavlidis [9]
introduced the scheme of polynomial surface fitting for
modifying the code vectors generated by SOFM which failed
to reduce the blockiness and dimensionality of the
reconstructed image. Lloyd [10] constructed an algorithm for
incremental update through competitive learning with higher
loss of data.
Image compression based on the combination of wavelet and
vector quantisation is done [11]. Wavelet compression along
with the comparison after applying its seven families is
worked by Jain & Jain [12]. Implementation of C means
clustering for codebook designing using fuzzy over wavelet
tree coefficients [13]. Image compression using various
wavelet approximations are proposed by DeVore et al [14].
Various applications of image processing use the combined
effects of SOM and Wavelets. Image compression can be
implemented by applying DWT over an image and SOM is
applied to its result [15]. Combination of DCT, DWT and
SOFM is also implemented, where SOFM is used to generate
codebook [16]. Compression in the combination of SPIHT and
SOFM has been implemented by Rawat and Meher [17].
Dandawate et al introduced a method of codebook generation
for vector quantisation with SOFM and DWT [18].
3. PROPOSED WORK
In the proposed method, we are using a combination of
artificial neural network and Discrete wavelet transform in
order to perform the compression. Type of the neural network
used differs from the existing methods. Here linear vector
quantisation has been used to train the input vectors. Input
image is splitted into non-overlapping blocks. Each block is
converted into one dimensional vector, which is given as the
input to the linear vector quantisation. As a result we get the
trained weight matrix and Indexes were obtained. The trained
output is given as the input to the discrete wavelet transform.
We get the low low, low high, high low and high level
components. The low low level components are encoded and
stored and other components were left.
In order to reconstruct the image, we process in inverse. We
first decode the stored low level components. The next step is
to perform the inverse discrete wavelet transform. We keep the
low components as it is and all other components like low
high, high low and high components as zero and perform the
inverse discrete wavelet transform. We then map the output of
the inverse discrete wavelet transform with the indexes
obtained as the result of linear vector quantisation. Now we
have the output in the form of vectors. Thus in order
reconstruct the image, the vectors are converted back into non-
overlapping blocks. Thus the reconstructed image is obtained.

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The flowchart for the above process is depicted as:
4. RESULTS AND DISCUSSION
Table 1: Comparison of PSNR values of various images with
SOM and LVQ.
IMAGE PSNR(dB)
SOM LVQ
Rice.png 25.43 27.73
Peppers.png 22.18 23.98
Coin.png 24.44 26.24
Cameraman.bmp 27.31 30.91
lena.bmp 26.80 28.45
Table 2: Comparison of MSE value of various images with
SOM and LVQ
IMAGE MSE
SOM LVQ
Rice.png 352.7238 289.3657
Peppers.png 537.7648 432.4961
Coin.png 478.2030 392.0730
Cameraman.bmp 163.9787 117.6012
lena.bmp 275.6821 198.5149
While comparing the results we get the better peak signal to
noise ratio and better mean square error values. Thus the
image is compressed in a better manner using linear vector
quantisation than that of using self organising maps.
5. CONCLUSIONS
In this paper we have introduced a new method for image
compression which uses artificial neural network and
transform coding together. Here the type of artificial neural
network used is linear vector quantisation and the type of
transform coding used is discrete wavelet transform. In the
algorithm an efficient codebook is obtained using linear vector
quantisation. While the discrete wavelet transforms blocks the
artifacts. The algorithm is very simple and computationally
less complex. This linear vector quantisation performs better
than many competitive networks like self organising maps.
The proposed algorithm achieves high peak signal to noise
ratio and reduced mean square error than many of the existing
technologies. Here both the texture informations and the edge
informations are preserved.
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