Multiwavelet Application In Image Coding And Video Coding

Wavelet theory provides a deep insight into the structure of subband filters. Based on the Project of National High Technique Research and Development (863), this paper focuses on balanced orthogonal filter construction, wavelet coefficients quantization and arrangement, wavelet image coding and video coding.Relationship of scalar wavelet and multiwavelet is discussed simply in this paper. The basic ideas of multiwavelet theory are given. For existence, uniqueness, and stability of scaling, some results are showed. To ensure to construct a multiwavelet exactly, regularity, approximation order, and factorization of scaling vector are also analyzed.There are at least 2 low pass filters for multiwavelet filter, if the two low pass filters have different spectral behavior, it can lead to unbalanced channels that complicate the vectorization. The polyphase method of vectorization leads to a mixing of the coarse resolution and details coefficients creating strong oscillations in the signal reconstructed from the coarse resolution only. To solve this problem, one method is using prefilter, the other presented in this paper is to construct balanced filters, and then construct balanced multiwavelet without any prefiltering, its spectrum is better than others filters.Trellis coded quantization (TCQ) benefitting from trellis coded modulation and set partitioning is studied, including TCQ state, state trellis, set partitioning, Veterbi algorithm, and the choice of code words. For independent uniform and Gaussian distribution data, TCQ can lead to very small mean square error (MSE) while TCQ's states increase, its performance improves 0.2~2dB than Lloyd-Max quantizer. Different weighted variance of subbands has allocated the corresponding rate; weighted average of subbands is equal to expected rate. Rate control of subband is to choose code words of quantizer or quantization step. A TCQ image coding method is presented based on multiwavelet transform and multithreshold, which using quad-tree to classify significant coeffiecients with 8 states and a new set partitioning. Testing shows the method can improve 0.03~0.14dB with respect to single threshold method.Analysis of multiwavelet transform shows, for ordinary transform, low frequency component is decomposed to high frequency component; it leads to the mixing of low and high frequency component while multiwavelets with prefilter or balanced multiwavelets are decomposed correctly. Statistics of mulitwavelet coeffiecients indicates 9/7 biorthogonal wavelet has the better distribution for smooth images (like Lenna), and multiwavelet can improve 1.45% than scalar wavelet for texture images (the magnitude of coeffiecients<8). Multiwavelet is more appropriate for texture image coding. Most of image energy goes to low frequency component. SPIHT (Spatial partitioning of images into hierarchical trees) achieves good performance by exploiting the spatial dependencies between coefficients in different subbands of a scalar wavelet transform, but the spatial dependencies do not be supported by multiwavelets. Examination of the coefficients for multiwavelet decomposition shows that there generally exists a large amount of similarity for each 2×2 blocks. To take advantages of the similarity, for different multiwavelet filters, this paper gives different methods to organize the multiwavelet coefficients, and then the SPHIT quantizer can benefit from it.In video coding, some video coding standards such as MPEG-2, MPEG-1, and H.264 are using discrete cosine transform (DCT). Though many new video coding techniques come out such as multiple reference picture motion compensation, variable block-size motion compensation with 4×4 block size, and in-the-loop deblocking filtering, transform is based on block, at very low bit rate, the DCT coders suffer block effect. Subband coding offers a possible alternative to DCT. As wavelet transform has a good performance to deblocking, combined with some highlighted features of H.264, this paper presents a video coding framework using multiwavelet transform (MWDT). Testing results show H.264 scheme performance exceeds MWDT framework, more stabile. For slowly moving frames, multiple references performance improves signal-noise ratio more than quickly moving frames. Loop filter leads to reconstructed image with better vision quality, and plays no contribution on signal-noise ratio.As the above discussed, this paper describes construction of balanced multiwavelet, multiwavelet transform, wavelet coefficients organization, TCQ, rate control, the selection of motion block size, and loop filtering. On these researches, the method of image compression has a good performance. Though this framework cannot do as well as H.264, it has potential of increasing the coding efficiency when the rate-distortion motion estimation technique is improved in the future.