| Nowadays multimedia applications are deeply embedded into all aspects of our lives with the development of computer and network technology. It has become an inevitable trend to provide users with multimedia services in the computer technology field. Compared with other traditional data applications, the most prominent feature of multimedia applications is the integration of audio, video and other types of media streams. These digital video signals generate extremely high data rates which can not be transmitted without first being compressed. Although currently there is rapid development in computer hardware, the hardware technique still can't meet consumer's requirements in video information. On the other hand, even if there are enough storage space and fast transmission speed, it is a waste of bandwidth without compression. The critical challenge for data compression is to reduce the bit rate without affecting picture quality. Therefore, video compression technology has been a permanent research focus in digital video technology.Color video consists of consecutive color images. There are correlations between the pixels of all the images, such as strong correlations in temporal domain in addition to the correlations in spatial domain and the correlations between the color components. All the correlations indicate that there are plenty of redundancies in video sequence. Video compression must be carried out using mathematical method. Multi-dimensional vector matrix theory can effectively decrease the redundancies between inter, intra frames and color spaces of video sequences, which is modeled in an entirely way like magic cube. Multi-dimensional transform is carried out in order to achieve good compression results with good image quality.The research group leading by professor Hexin Chen have been studying multidimensional transforming model in recent years. They proposed multidimensional theory and enriched the theory in image and video coding. Great success is achieved in image and video coding, such as 3D-DCT and 3D-WDCT. However, there are many different multiplication rules defined in the former multidimensional theory and it is not suitable to carry out in application, our group recently proposed a new theory—multi-dimensional vector matrix theory, which enriched the theory on multi-dimensional matrix and resolved the problem of multiplying matrices of different orders. Based on the theory, deep researches are carried out in video coding.Supported by the National Nature Science Foundation Project of China 'Research on multi-dimensional vector matrix orthogonal transformation codec in color video'and National Nature Science Foundation International cooperation Project of China'Ubiquitous Computing based on Synchronous Coding for Mixing Video/Audio', this thesis analyses the application requirement and key problems existing in image and video coding, discusses multidimensional signal processing technology. This thesis carries out the research on multidimensional vector matrix DCT integer transform, quantization and scanning method, multidimensional model in order to make foundation on effective codec.Discrete cosine transform (DCT) is widely used in the field of image and video coding. The transformation is significant in all sub-optimal performance which can remove the image elements'correlation in the transform domain in highly efficient way, so it makes the foundation in compression. However, floating DCT will produce accumulating errors because the floating operation's precision of computer is finite. Especially mismatch will happen in the decoder. So the integer to integer transform reduces the accumulating errors and improves the encoding efficiency. Because integer multiplication can be replaced by addition and shift operation, it can improve efficiency and reduce operation complexity. This thesis extends the theory of multi-dimensional vector orthogonal transformation matrix and presents a new 4-D Order-4 DCT integer transform operator based on the theory of multi-dimensional vector matrix discrete cosine transform (MD-VMDCT). Meanwhile, the orthogonality of the operator and energy concentration are verified in the paper. Also the comparison between the integer and the float 4D-VMDCT is carried out. At last the video sequence is compressed by using our approach. The experimental results show that the algorithm is correct and effective. It is better than H.264/AVC under the same conditions and it is slightly lower in performance compared with floating 4D-VMDCT.This thesis proposed 4-D Order-4 DCT integer transform operator and got effective performance in video coding. However, the 4D-VMICT coefficients have been encoded using vector quantization which heavily depends on the code book. It is not widely used in video coding and not compatible with international standards. So this thesis proposes a technique for generating the quantization cube and an improved zigzag scanning method suitable to MD-VMICT codec after studying the statistical properties of the DC and AC coefficients. An exponential function is used to quantization and it is verified to 2-exponential function in order to easily carrying out by shift operator. After determining the proper parameter by experiments, the proposed quantization and scan order are tested on various standard test video sequences. The experiments show the wide adaptability. Also the comparisons are carried out with the literature and MPEG-4, whose experiment results show superiority than the literature and MPEG-4. The comparisons between MD-VMICT and H.264/AVC show potential advantages at low bit rate with high activities sequences.The theory of multi-dimensional vector matrix requires dividing the video data, so how to express the multi-dimensional vector matrix efficiently and find the correlation among the various components are the basis for the follow-orthogonal integer transform. We have modeled the three dimension vector matrix in the former study by use of the row, the column and the time components. We have made MD vector matrix orthogonal transformation and obtain good compression. Based on 3D model, this thesis goes on studying 4D model method, This thesis proposes 4D modeling technique in details for 4D vector matrix DCT integer transform (4D-VMICT) codec. The physical sense of 4D model is described with illustrations. Two models which are cumulate model and sampling model are present which can eliminate temporal redundancy, spatial redundancy, and statistical redundancy among the pixels in video sequence by use of the super concentration of the 4D-VMICT. Then an improved quantization and zigzag scanning method suitable to 4D-VMICT codec are proposed based on the properties of codec. After determining the proper parameter by experiments, the proposed method is tested on various standard test video sequences. The experiments show the efficiency and the wide adaptability. The comparisons which are carried out with the literature and MPEG-4 show the method's superiority. Also the comparisons between 4D-VMICT and H.264/AVC show potential advantages at low bit rate with high activities sequences. At last, different properties about two models are summarized in the experiment results. The results show that sampling model can eliminate redundancy among the pixels more effective than cumulate model. Meanwhile, sampling model has better object result than cumulate model. The thesis proposes 3D-VMICT codec and 4D-VMICT codec, which expands the applications of multi-dimensional vector matrix theory in color image and video compression field.
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