IEEE IPAS'14: INTERNATIONAL IMAGE PROCESSING APPLICATIONS AND SYSTEMS CONFERENCE 2014
Color Image Compression Based on Wavelet Transform and Support Vector Regression WSVR for Color Image Compression
* 'i' '!' Nadia Zikiou , Mourad Lahdir , SoItane Ameur Laboratoire d' Analyse et de Modelisation des Phenomt'mes Aleatoires (LAMPA), Departement d'Electronique, Universite Mouloud Mammeri (UMMTO) Tizi Ouzou, Algerie * Email:
[email protected] t Email:
[email protected] ·;· Email:
[email protected]
Abstract- Recent years have seen tremendous increase in the production, transportation and storage of color images. A new method for lossless image compression of color images is presented in this paper. This method is based on wavelet transform and support vector machines (SVM). The wavelet transform is applied to the luminance (Y) and chrominance (Cb, Cr) components of the original color image. Then SVM regression dependence could learn from training data and compression achieved using less training point (support vector) to represent the original data and eliminate redundancy. In addition, an effective entropy coder based on run-length and arithmetic encoders is used to encode vector and weight support. Our compression algorithm is applied to a test set of images of size 1024 * 1024 encoded on 24 bits. To evaluate our results, we calculated the peak signal noise ratio (PSNR) and their ratios datasets compression (CR). Experimental results show that the performance of the compression algorithm to achieve much improvement. Keywords- Color Image compression; Wavelet Transform; Support
Vector
Regression
(SVR);
Run-length,
Arithmetic
coding, PSNR.
I.
INTRODUCTION
From early days to now, the basic objective of image compression is the reduction of size for transmission or storage while maintaining suitable quality of reconstructed images. For this purpose, many compression techniques, i.e. , scalar/vector quantization, differential encoding, predictive image coding, transform coding have been introduced. Among all these, transform coding is most efficient especially at low bit rate [1].
978-1-4799-7069-8/14/$31.00 ©2014 IEEE
SVM is a learning system that uses a hypothesis space of linear functions in a high dimensional feature space to estimate decision surfaces directly rather than modeling a probability distribution across training data [2]. It uses support vector (SV) kernel to map the data from input space to a high-dimensional feature space, which facilitates the problem to be processed in linear form. SVs are samples that have non-zero multipliers at the end of optimization process which is referred to equation. SVM always finds a global minimum because it usually tries to minimize a bound on the structural risk, rather than the empirical risk [3], [4], [5] & [6]. For past few years Discrete Wavelet Transform (DWT) is used for image compression which is a powerful technique for compression due to its multi resolution feature, scalability and flexibility. Jio [7] suggest a compression method by combining Discrete Wavelet Transform along with SVM, it is observable that it removes blocking artifacts and the quality of the image gets improved. Wavelet Transform segregates the information present in the image into approximate and detail signals. The approximation signals display pixel values of image and detail signal displays the horizonta� vertical, and diagonal details of an image. More over wavelets provides transaction between frequency and time localization [8]. Based on this, SVM is applied on the wavelet coefficients for further compression by removing the redundancy which results in better quality of image and higher compression ratios [9]. In this paper, we present a new scheme for color image compression based on the 20 Discrete Wavelet Transform and Support Vector Regression (SVR). First, the image is converted to YCbCr format and the biorthogonal 4. 4 wavelet transform is applied for luminance (Y) and chrominance (Cb,Cr) components. The lowest sub-band of wavelet coefficients (approximations) is encoded by differential pulse code modulation (DPCM). The fmer scale sub-bands (details) are compressed by SVM regression which approximates the Wavelet coefficients using a fewer support vectors and weights. And some of the finer scale sub-bands are discarded directly due to containing a little amount of energy and having little noticeable effect on the image
2
IEEE IPAS'14: INTERNATIONAL IMAGE PROCESSING APPLICATIONS AND SYSTEMS CONFERENCE 2014
quality. At last, these coefficients are quantized and encoding by Run-length and Arithmetic coders. The remainder of this paper is structured as follows: Section II discuses 20 - OWT and theory used in proposed image compression. Section III describes SVM Regression. The sections IV and V present datasets and proposed method respectively. Section IV shows experimental results. Conclusion and orientations for future works are discussed in Section nv.
II.
DISCRETE WAVELET TRANSFORM
W(k, I)
=
1
+00
(5)
f(t) IJIk1(t)dt
-00
and the inverse transform as +00
f(t)
=
+00
I I d(k, l)Z-k/2 IJI(Z-kt
-
k=-ool=-oo
The values of the wavelet transform at those represented by
Compressions based on Wavelet techniques provide substantial improvement in picture quality at lower bit rates [10].
d(k, I)
=
W(k, l)le
a
I)
(6)
and Tare
(7)
Iff(t) is any square integral function satistying
(1) The continuous time wavelet transform of f(t) with respect to a wavelet is defined as
W(a, T)
=
1
+00
-00
fCt)
1 fT""::T vial
(t T) 1JI* - dt a
(8) (2)
The wavelet may be defmed as
(3) The function, referred to as the mother wavelet, satisfies two conditions - it integrates to zero and is square integral, or has fmite energy.
It is preferred to represent f(t) as a discrete superposition sum rather than an integral for digital image compression. Equation (3) now becomes
(4)
=
and the inverse discrete time wavelet transform as +00
Where the real variables a and T are dilation and translation parameters, respectively, and * denotes complex conjugation [11].
Where a both integers.
The d(k, I) coefficients are referred to as the discrete wavelet transform of the functionf(t). If the discretization is also applied to the time domain letting t = mT, where m is an integer and T is the sampling interval chosen according to Nyquist sampling theorem, then the discrete time wavelet transform is defined as
2k and T =2kl for discrete space with k and 1
The corresponding wavelet transform can be rewritten as
f(m)
=
+00
I I d(k, l)2-k/2 1JI(2-km
k=-ool=-oo
-0
(9)
The decomposition of an image using discrete wavelet transform comprises of a chosen low pass and a high pass filter, known as Analysis filter pair. The low pass and high pass filters are applied to each row of data to separate the low fr�ency and the high frequency components. These data diil} be sub-sampled by two. The filtering is then done for each column of the intermediate data finally results in a two dimensional array of coefficients containing four bands of data, known as low-low (LL), high-low (HL), low-high (LH) and high-high (HH). Each coefficient represents a spatial area corresponding to one-quarter of the original image size. The low frequencies represent a bandwidth corresponding to 0
