Adaptive Vector Qualification Coding on Wavelet Information for data Compression
K. Kittayaruasiriwatx, F. Cheevasuvitx, A. Somboonkaewxx, K. Dejhanx, s. Chitwongx, S. Mitathax and S. Wongkharnxxx
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.
