Research Of Karhunen-Loeve Transform Based On Multi-dimensional Vector Matrix

As the the rapid development of network technology and increasingly matureof digital communications, the dependent on image and video for people ishigher. Image video as the most informative vector has been widely applied invarious fields. However, the amount of uncompressed image data and videosignal is very large, image and video has been compressed to meet therequirement of the storage space and transmission bandwidth, therefore, imageand video compression technology is the key to problem-solving. Based on themulti-dimensional vector matrix model theory of image and videocompression encoding technology is one of the more effective compressioncoding methods in the multimedia field. K-L transform leads to continuousrandom process as a series expansion by Karhunen and Loeve, as the statisticalproperties of each bath of images have different transform nuclear matrix. K-Ltransform is the best transform of the image compression coding technology,correlation between pixels in the image signal can be completely eliminated.Our laboratory has proposed the model of multi-dimensional vector matrix,and has summarized the guidelines for the total definitions and basicmathematic of the multi-dimensional vector matrix. This paper integrates theknowledge of linear algebra and multi-dimensional vector matrix model,proposes innovatively definition and related properties of themulti-dimensional vector adjoin matrix, determinant and inverse matrix, andimproves the related mathematical concepts in the process of themulti-dimensional vector matrix inverse, then using the multi-dimensionalvector matrix multiplication rules to verify the correctness of the mathematicaldefinition. Meanwhile, we have defined eigenvalues and eigenvectors of themulti-dimensional vector matrix, preparing for K-L transform process of themulti-dimensional vector matrix. Finally, integrating the algorithms of K-Ltransforms and multi-dimensional vector matrix model can get the K-Ltransform of the multi-dimensional vector matrix. Multi-dimensional vector matrix by K-L transform has verified the orthogonality and the concentrationof energy of multi-dimensional vector matrix. Therefore this method achievedthe K-L transform of multi-dimensional vector matrix under the condition ofminimum mean square error and provided the solid mathematical foundationfor the multi-dimensional digital signal processing.Then the experiment uses tool to the Visual C++6.0programmingmulti-dimensional vector matrix inversion process and the K-L transform ofmulti-dimensional vector matrix, the experimental results were summarizedand analyzed. This paper chooses8-viewpoint, YUV format, then divides theY、U、V component into cubes separately, then combines again the eight viewsdata and K-L transform. Because the ordinary video data is3D, this paperintroduces the multi-view of video data, which is four-dimensional data.Finally, the result of K-L transform could be analyzed about orthogonality andenergy concentration, the K-L transform in the minimum mean square errorconditions with the other transforms completely restores the original image.This paper applies the theory of multi-dimensional vector matrix tomulti-video K-L transform innovatively, handles any order of themulti-dimensional vector square matrix and achieves the best transform ofvideo data, but also brings huge computation and computational complexity.From the experimental results verify the effectiveness and feasibility of theproposed algorithm, this algorithm is not completed and further researched andexplored, and prospects continue improving in the direction of this algorithm.This paper is supported by the National Science Foundation of China under...