The Research On Optima Transformation Based On Theory Of Multi-dimensional Vector Matrix

Video image is the most abundant and intuitive information carrier. And it fills with all areas of people’s life. Statistics show that the information provided by the visual system presumably accounts for 3/4 of all the external information obtained by the human sensory organs. With the continuous improvement of video requirements, the amount of video transmitted in real time is also increasing. Our pursuit is how to transmit more and better video in the limited bandwidth. It is also the research focus in this field. Transform encoding, as the core of the video compression, is an important method. In the paper, we mainly study the transform coding.Transform coding is usually the unitary transformation of the image. Then the transform results are quantified. Finally the quantization results are coded. Under the premise of ensuring the quality of image viewing, transform coding can compress the transmission and storage of data to the maximum extent. Transform coding has been widely used in various video image coding standards. But, the current application of the transform coding for single frame image, it is encoded in the 2 dimensional space domain, it can’ t use the time domain correlation.As a new theory and technology of video data, the theory of multi-dimensional vector matrix has been developed greatly in recent years. Multi-dimensional vector matrix can be used to unify the space dimension, color dimension, time dimension and visual angle of the video image in a model. Multi-dimensional vector matrix is more conducive to the extraction of the correlation between the various dimensions, to remove redundant information.In order to seek a multi-dimensional vector matrix theory for the optimal transformation, this paper analysis the one-dimensional optimal transformation under mean square error and sub optimal transformation-- DCT transform. Based on the multi-dimensional vector matrix, the multi-dimensional KL transform and the multi-dimensional DCT transform are studied:(1) Multi-dimensional KL transform: in order to adapt Karhunen-Loeve(KL) transform to multi-dimensional data, and at the same time to find out the optimal transformation of multi-dimensional vector matrix. In this paper, MKL transform based on the theory of multi-dimensional vector matrix is proposed. Firstly, multi-dimensional covariance matrix is defined combining multi-dimensional vector matrix theory, and the multi-dimensional characteristic matrix vector is solved. Then MKL transform is defined and it makes multi-dimensional data to map to projective space. The experimental results show that the KL transform is a special case of the MKL transform in one dimension. For the 3D video data, the MKL transform can achieve a complete solution, and the average energy concentration ratio(EPE) is 99%.(2) Multi-dimensional DCT: In order to make multi-dimensional DCT transform in multi-dimensional plane are more close to the optimal transform, this paper makes a further research work on the multi-dimensional DCT transform. Firstly, the energy characteristics of multi-dimensional DCT transform was studied by simulation experiment, and the energy of multi-dimensional DCT is focused on the folding plane. Then the tree structure for image coding is presented, which is suitable for multi-dimensional DCT. Finally adaptive multi-dimensional DCT based on the energy measure is proposed. The simulation experiment results show that the efficiency of the algorithm is better than the multi-dimensional DCT.Firstly, MKL transform is proposed and its multi-dimensional optimality is alsoFirstly, MKL transform is proposed and its multi-dimensional optimality is also proved by theoretical derivation. Then through the research of multi-dimensional DCT, adaptive multi-dimensional DCT based on the energy measure is proposed. The performance comparison shows:.(1) MKL transformation is the optimal transformation under multi-dimensional mean square. For the multi-dimensional data, the MKL transform can achieve a complete solution. However, the complexity and time spent of the algorithm is high.(2) Adaptive multi-dimensional DCT based on the energy measure has excellent compression performance. It is close to the optimal transformation. The algorithm achieves better results on the time and compression effect.