| With the fast development of communications technology, diverse communications appear, digital video service is widely used as it has so many advantages, easy to understand, good transmission and anti-interference quality, high reliability, easy encryption and so on. However, as the digital data are so large that wide bandwidth and large storage space are needed, so the compression of digital video is imperative. Orthogonal transform coding is a very efficient compression method, because the direct current and low frequency regions take up a great proportion, while high frequency regions occupy small proportion in most of images. The image signal is transformed from spatial domain into frequency domain. Under the rule of the least mean square error, discrete cosine transform is the quasi-optimal transform coding method, as its basis vector is approximate to the characteristic vector of covariance matrix of natural images. Meanwhile, DCT is real arithmetic and there is fast calculation method, so it is widely used in international video and image compression standards.DCT takes advantage of the correlation between pixels to compress. Theoretically, all image data should be transformed at one time to eliminate the whole correlation, but the computational complexity is very large. Therefore, before transformation, image is segmented into many small blocks, the shape of which is normally square. The size of block is generally chosen as the nth power of 2 to convenience for fast calculation. Customarily, it is thought that when the size of block is 8, the correlation between pixels is the highest, so the size of block of fixed partition transformation is normally chosen as 8. Unfortunately, there are different statistical characteristics in different aeries of image. On the one hand, if the image content in some region is very similar, the correlation between the pixels in this region is high, then transformation with larger size of block can get higher energy compaction; on the other hand, if the image content is different in some region, transformation with larger block size may cause ring effect, using smaller size block is helpful to detail preserving. The technique of adaptive coding can well deal with this problem.When the bit per pixel is less than 1, adaptive coding will play an important role in image compression. Adaptive transform core is that the image is divided into various rectangular blocks according to the image content, and then transformed with corresponding block. It was appropriated when the block size is 4,8, or 16, moreover, the type of size had better not go beyond 3 in variable block size transform coding.Three dimensional cosine transform is considered as the replacement technique of motion compensation.3D-DCT can make full use of the correlation between several frames to compress, while motion compensation can only eliminate the correlation between two frames. Moreover, as the structure of 3D-DCT is non-recursive, it avoids infinite spread of the transmission errors. Meanwhile, the encoding and decoding complexity of 3D-DCT is the same, which is very suit for real time coding. On the condition that the gross amount movement is low,3D-DCT is very efficient. The disadvantage of 3D-DCT is that it has longer coding delay and larger memory space requirement, but with the rapid development of computer hardware technology, the computational speed is more and more fast, there are more and more researches focusing on 3D-DCT.At present, there are some problems about the study of 3D-DCT:1. As there are no unify definition of the operation approaches between multidimensional matrixes, the study about matrix format of three dimensional discrete cosine transform is very scarcity.2 There are too many block partion riterions.3. There is no concrete reference model (RM) of human visual system (HVS) for 3D quantization.4. The entropy method for 3D scanned coefficients is the traditional RL-VLC method in JPEG.Regarding of the first problem, Sang proposed multidimensional vector matrix (MDVM) theory, which is about the operation approaches between multidimensional matrixes, and imitates the operation format between 2D matrixes. The representation is concision, the form is easily understand, and the operation complexity is medium, and it is easy to be extended to even more high dimensional matrix operation. Hu applied the theory into the field of orthogonal transform compression of color image, derived the transform core matrix of 3D-MDCT.About the second, to reduce complexity, a fast scheme using a picture activity measure is proposed. In lossy coding, most of the gray-level histogram statistics of the images do not have any direct effect on the lossy coding performance, and image activity measure is the only feature that has a negative correlation with the PSNR value, gradient-based activity measure is the best measure and it is not only very effective in differentiating between various images but also correlates well with the PSNR. Moreover, as the direction of energy compaction of DCT is along to the vertical and horizontal, the vertical gradient and horizontal gradient can well reflect energy compact capability.For the third, according to the key fact which affects quantization designed a lot:1. The probability distribution function of transformed coefficients is helpful to the design of minimum distortion quantization.2. The first-order low-contrast modulation transfer function of human visual system model.Combined the two mentioned to construct the three dimensional quantization matrix. The last, the RL-VLC method in JPEG is improved, a new entropy method that based on nonzero coefficient level and zero coefficient run length level, named LL-VLC is proposed, and according to the simple model based on context, encoding M X N X L coefficients one time, the table code cost is medium, and there are good potential to entropy coding in even higher dimensional orthogonal transform.To some extent, this paper proved the effectiveness of multidimensional vector matrix orthogonal transform in image compression field, but the theory is in its early research stage, there are still many details need to study and further research. For example, the research of fast algorithm based on the multi-dimensional discrete cosine transform system, or combined with the classical international compression standard and latest technique. |
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