Research On Color Image And Video Coding Based On Multi-dimensional Matrix Theory

In recent years, with the development of computer and network techniques, the applications related to digital image and video become more and more important and widespread in daily life. A professional image and video processing server, or a personal computer, or a personal digital assistant, even a state-of-art cellular phone has the computational and technological capabilities of viewing and editing of digital image and video. Digital television broadcast and internet TV have become reality. In the meantime, the volume of image and video data need to be stored and transmitted increases explosively due to the growing image and video services. Although the storage techniques improve and the bandwidth of the network increases, an effective image and video compression method is required, which is one of the best schemes to solve the storage and transmission problems of the massive multimedia information. Image and video compression is one of the most popular research topics in these years.In RGB color space, there exist correlations in spatial domain between the pixels of color image, and so do the color components of color image. Color video consists of consecutive color images. Therefore, there exist strong correlations in temporal domain in addition to the correlations in spatial domain and the correlations between the color components. According to the information theory, these correlations indicate that there are redundancies in the image and video data. The signal compression can be implemented by using some kind of mathematical methods to remove these redundancies. The multiple dimensional matrix theory and the multiple dimensional matrix DCT are effective mathematical methods used in image and video compression area. The multiple dimensional matrix theory is adopted to describe the color image and video in a unified mathematic model. Base on this model, the multiple dimensional matrix DCT is employed to effectively remove the correlations of color image and video in spatial domain, temporal domain and the correlations between color components, which makes it possible to compress the color image and video at a high compression ratio. In this paper, the multiple dimensional matrix theory is improved and expanded. The decomposition operation of the multiple dimensional matrix theory is proposed and defined.The multiple dimensional matrix theory was firstly used in color image compression system. The 3D matrix WDCT color image compression system (3DM-WDCT) is one of the representatives based on this theory. Color image compression methods based on three-dimensional matrix DCT (3D-MDCT) normally use fixed size matrix segmentation and fixed size transform. In 3DM-WDCT, 8×8×3 submatrix is adopted, in which the first two dimensions represent spatial position and the third dimension represent three color components. However, different image has different statistical property in practical application. Hence, fixed size segmentation can not effectively exploit the image redundancy because the different areas of an image have different statistical properties. In this paper, a color image compression approach using variable matrix-size three-dimensional matrix DCT (VMS-3DMDCT) is proposed. The proposed approach divides the original color image into variable-sized sub three-dimensional matrices according to the activity characteristics of the original color image. In the smooth field of a image, the activity is small; in the area, where includes details and edges, the activity is big. By the encoding, the input image is divided into 16×16×3 macro submatrices. The activity characteristics of each macro submatrix is calculated, which is the criterion to decide whether a macro submatrix will be further divided into smaller submatrix or not. Accordingly, the variable-sized 3D-MDCT is applied to the corresponding-sized sub 3D matrix. Transform coefficients are quantized using non-linear scalar quantization and further compressed using entropy coding. The proposed method utilizes the statistical property of color image to achieve high compression efficiency. Moreover, 16×16×3 quantization table for 16×16×3 macro submatrix and 4×4×3 quantization table for 4×4×3 submatrix are defined based on the brightness quantization table of JPEG.As another application example of multiple dimensional matrix theory, four-dimensional matrix DCT (4D-MDCT) is applied to color video compression. 4D-MDCT is completely reversible in theory. However, because the float operation's precision of computer is finite, float transform produces mismatching in the decoder. As a result, the original signal can not be completely reconstructed. Integer to integer transform can avoid this kind of mismatching. According to the definition of 4D-MDCT, it can be proved that the transform core matrix is a unitary matrix. Based on the matrix factorization theory for reversible integer transform and the decomposition operation property of 4D-MDCT, the integer to integer 4D-MDCT is implemented by factorizing the float 4D-MDCT into reversible integer transform. In this paper, a color video compression scheme is proposed based on the integral implementation of 4D-MDCT. Firstly, the proposed method utilizes the four-dimensional matrix model to describe the color video. Then the integer implementation of 4D-MDCT is performed and the integer transform coefficients are vector quantized and entropy coded.The experimental results show that the compression efficiency of the proposed VMS-3DMDCT algorithm has great advantages than JPEG at low bit rate. The proposed algorithm improves the PSNR up to 5 dB compared to JPEG. The compression performance is also better than three dimensional matrix transform coding based on YC sub matrix. For the case of proposed video compression scheme based on integral implementation of 4D-MDCT, the experimental results indicate that PSNR of the reconstructed images based on integer scheme is improved more than 1dB than that of the reconstructed images based on float scheme. The quality of reconstructed images of integer scheme is improved also in subject. Compared to H.264 without B frame, the proposed method outperforms H.264 when the size of codebook is equal or great than 512. Otherwise, H.264 has a better performance than the proposed method. The proposed methods in this paper improve and expand the applications of multiple dimensional theory in color image and video compression field. Consequently some new research topics are provided.