Adaptive Vector Qualification Coding on Wavelet Information for data Compression

Adaptive Vector Qualification Coding on Wavelet Information for data Compression

K. Kittayaruasiriwat^x, F. Cheevasuvit^x, A. Somboonkaew^xx, K. Dejhan^x, s. Chitwong^x, S. Mitatha^x and S. Wongkharn^xxx
^xFaculty of Engineering King Mongkut's Institute of Technology Ladkrabang,
Bangok 10520, Thailand
^xxElectro-optics laboratory, National Electronics and Computer Technology Center,
73/1 NSTDA Building, Ministry of Science Technology and Environment Rama VI Road,
Rajtavee, Bangkok 10400, Thailand
^xxxFaculty of Engineering, Mahanakorn University of Technology,
Bangkok 10530, Thailand

Abstract
Due to its advantages for images transmittly in community in communication network, wavelet transform is one of the well-known method for image compression. Fore one state of wavelet transform, The primary subband images consist of one low-pass and three high-pass. These subband images are referred as LL, LH, HL and HH. For image compression by a traditional method, the high frequency subband image (HH) will be discarded. However, the constructed image from LL, LH, HL will be lost the detail of edges and given high mean square error. To solve this problem, this paper proposes a method of adaptive vector quantization coding on wavelet information obtained from the two state transformation. All obtained 16 subband images were also employed in order to decrease the mean square error and preserve the compression bit rate in the same time. The lowest frequency subband image will be assigned 8 bits for encoding each pixel. Then, a.c. energy of each subband image, from the remaining 15 subband images, will be calculated by using discrete cosine transform. After that, each subband image, from the remaining 15 subband images, will be calculated by using discrete cosine transform. After that, each of them will be sorted from minimum to maximum. The accumulation of a.c. energy from 15 subband images will be divided into 4 classes. The first two lower energy classes will be encoded with zero bit. The third containing energy from 50% to 75% will be encoded with 256 code vectors for 4x4 pixels block size. This vector quantization code book provides the bit rate of 2 bits per pixel. Then the total subband image will be calculated to total bit rate. If the total bit rate is less than the given bit rate, the highest energy subband image of the third class will be pushed up into the fourth class. So, this subband image will be encoded with 2 bits per pixel. On the other hand, if the total bit rate is greater than the given bit rate, the lowest energy subband image of the third class will be pushed down into the second class for zero bit encoding. The bit rate adjustment process will be iteratively adapted in order to prevent the obtained bit rate greater than the given bit rate. The result image from the proposed method will be clearly improved by the mean square error (MSE).

Introduction
The image compression techniques become more and more useful for reducing the number of bits per picture element while retaining good quality. The compressed image will be caused a reduction of storage size and retransmission cost, these benefits are clearly appeared in manipulation of remote sensing data. There are so many techniques in order to compress an image. But in this paper, we propose a method of adaptive vector quantization coding or wavelet information or data compression. The details can be described as following paragraphs.

Wavelet transform, vector quantization and discrete cosine transform
Wavelet transform is a powerful tool in image analysis. Since the transformed data is composed of spatial domain data and frequency domain data[1]. For one state of wavelet transform, the transformed images will be combined of one lower frequency subband image and three higher frequency subband images. These subband image are assigned as LL,LH, HL and HH. To compress an image from wavelet transformed data, the subband of high frequency image (HH) will be omitted in the reconstruction process. However, for some structure of image, the high frequency subband image may be contained of significant a.c. energy. The compressed image, obtained by neglecting the high frequency subband image may be contained of significant a.c. energy. The compressed image, obtained by neglecting the high frequency subband image, will introduce and important mean square error. To improve the mean square error, all subband image must be considered. Each a.c. energy of high frequency subband image must be calculated and classified in order to provide a proportion of bit rate. Therefore, the subband image with high a.c. energy will be encoded with high bit rate. While the subband image which have low a.c. energy will be encoded with low bit rate or may be discarded.

By using vector quantization; image coding has demonstrated as a powerful method for image compression[2]. Therefore, in this paper, the vector quanitication method is applied to the subband images obtained from wavelet transform. For a given bit rate of compressed image, each subband image has been assigned the number of bit per pixel(bpp) which is calculated from the proportion of a.c. energy. The codebook for encoding and decoding will be provided into 2 groups. The first group has 256 code vectors for 2x2 pixels block size which provides the bit rate of 2 bpp. While the second group has also 256 code vectors but for 4x4 pixel block size which provides the bit rate of 0.5 bpp. These two groups of codebook will be assigned to any subband image in order to maintain the given bit rate. The first group of codebook is applied to the subband image in order to maintain the given bit rate. The first group of codebook is applied to the subband image with high a.c. energy, while the second group is employed in the subband image with low a.c. energy.

The a.c. energy of each subband image will be calculated by discrete cosine transform [3]. All a.c. energy values are sorted form minimum to maximum. These energy values will be almost 25% of the total energy. For the two lower classes of a.c. energy almost 25% of the total energy. For the two lower classes of a.c. energy will be encoded with zero bit. The third class will a.c. energy from 50% to 75% will be encoded with 0.5 bppusing the second group of vector quantizaion codebook. While the fourth class with the highest a.c. energy will be encoded with 2 bpp using the first group vector quantization codebook.

Adaptive vector quantization coding
For a given bit rate of compressed image, the subband image with the highest possible amount of the total a.c. energy in the fourthe class will be encoded by the given bit rate and the empoloyed bit rate is calculated. If the remainder bit rate is great enough, the next subband image with highest possible amount of the remaining a.c. energy in the fourth class be encoded by the book with 2 bpp, and so on. When the remainder is still great enough even all subband image of the fourth class are alredy encoded, then the subband image with the higher a.c. energy in the third class will be push up into the fourth class for encoding by the encoding by the codebook of bit rate 2 bpp. However, for the low bit rate compression, all subband image in the fourth class can not encoded with the bit rate 2 bpp. Therefore the subband images with lower a.c. energy will be pushed down into the third class for encoding with the bit rate 0.5 bpp. This may be caused zero bit encoding for the subband images in the second and the first class.

The encoding process is iteratively treated in the third class by using the codebook with 0.5 bpp.

By the mentioned procedures the codebook with different bit rate will be iteratively adapter in order to prevent the obtained bit rate for not greater than the given bit rate.

Experimental result
The two states of wavelet transform is applied to an image, then 16 subband images will be obtained as shown in Fig.1.

Fig. 1 Two states of wavelet transform
The subband image with the lowest frequency (LLLL) is contained the main energy of original. Therefore, this subband image will be encoded with 8 bpp, while the recently method for encoding the wavelet transformed data using vector quantization in [4] and [5] are shown in the Fig. 2. These two methods give a fixed pattern of number of bit per pixel for each subband image.

	Method [4]	Method [5]	Proposed method
JERS-1	60.1278	55.3232	43.4675
Land sat	47.6863	44.2886	35.9365
Lena	30.2816	27.1235	16.84519

Table 1 Mean square error
The testing images with the size of 512 X 512 pixels as shown in Fig. 3(a), 4(a) and 5(a) is used for the experiments. The proposed method is applied to the image in order to obtain the compressed image with the bit rate 1.03125 bpp. The reconstructed image is shows in Fig. 3(b), 4(b) and 5(b). The mean square error of the proposed method and the method of [4] and [5] in the table 1.

8 bpp	VQ 2bpp Codebook size=2x2 N=256	VQ 0.5 bpp Codebook size=4x4 N=256
VQ 2bpp Codebook size=2x2 N=256	VQ 0.5 bpp Codebook siez=4x4 N=256
VQ 0.5 bpp Codebook size=4x4 N=256		0 bpp

(a) Encoding pattern of [4]

8 bpp	VQ 2 bpp Codebook size=2x2 N=256	VQ 0.5 bpp Codebook size=4x4 N=256	VQ 0.5 Codebook size=4x4 N=256
VQ 2bpp Codebook size=2x2 N=256	VQ 0.5 bpp Codebook size=4x4 N=256	0 bpp	VQ 0.5 bpp Codebook size=4x4 N=256
VQ 0.5 bpp Codebook size=4x4 N=256	0 bpp	0 bpp	VQ 0.5 bpp Codebook size=4x4 N=16
VQ 0.5 bpp Codebook size=4x4 N=256	VQ 0.5 bpp Codebook size=4x4 N=256	VQ 0.25 bpp Codebook size=4x4 N=16	VQ 0.5 bpp Codebook size=4x4 N=256

(b) Encoding patter of[5]
Fig .2 Fixed patterns of vector quantization encoding for the wavelet transformed data

(a) Original Image

(b)Compressed image
Fig.3 JERS-1 image

(a) Original Image

(b) Comprssed image

Fig.4 TM image from Land sat

(a) Original image

(b) Compressed image

Fig.5 Lena image
Conslusion
The result from porposed method has been shown an important improvement in image fidelity or image quality. Since an image can compose of the edges with different gradient directions. Therefore, the a.c. energy from the corresponding edges is unpredictable. The method of fixed pattern of bit rate always can not match with the high a.c. energy information. Unlike the proposed method, the high a.c. energy subband image has been sorted before encoding it with higher bit rate. The mean square error from the compreesed image is then reduced as shown in the table 1.

Acknowledgement
The authors would like to thank the National Research Council of Thailand (NRCT) for provding the satellite images and Mr. Suchati nuchpitak for proving the manuscript.

Mr. Suchati is with the Department lf languages and Social Science, Faculty, Faculty of Industrial Education, King Mongkut's Institute of Technology Ladkraband, Bangkok, Thainand.

Reference

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