The Structure, Design and Application of M-band Symmetric Wavelets and Filter Banks

具有对称基函数的小波变换正成为下一代静止图像压缩标准。 小波方法在低比特率下优于当前的JPEG标准，并且随着比特率的降低而优雅地降级。 新的M通道对称小波用于图像和视频编码器，特别注意量化策略和运动补偿。 本论文主要研究线性相位正交与双正交M通道滤波器组与M带对称小波的理论、设计与应用。 多速率滤波器组是子带和小波分解以及频域/时域复用的基本构建块。 正在解决的理论问题的研究，包括线性相位M通道滤波器组和小波的结构，包括一个全面的理论允许的长度，最小的结构参数化和快速计算，以及二维信号处理的映射。 小波滤波器的设计标准也正在解决，包括消失的时刻，平滑性和非负的尺度函数，不等长的过滤器。 研究人员正在研究上述应用程序的图像，视频和地震数据，多载波调制和多尺度特征检测的感知为基础的数据压缩。 他们还在研究使用M波段小波变换进行多音调制。 M通道滤波器组的频率划分特性可实现双绞线铜线和混合光纤同轴电缆等通道的高效率，同时降低对窄带干扰的敏感性。

The wavelet transform with symmetric basis functions is emerging as a next- generation standard for still-image compression. Wavelet methods outperform the current JPEG standard at low bitrates, and degrade gracefully with decreasing bitrate. The new M-channel symmetric wavelets are used in image and video coders, with particular attention to quantization strategies and motion compensation. This research is addressing the theory, design, and application of orthogonal and biorthogonal linear-phase M-channel filter banks and M-band symmetric wavelets. Multirate filter banks are the fundamental building blocks for subband and wavelet decompositions, as well as frequency-domain/time-domain multiplexing. Theoretical questions being addressed by the research include the structure of linear-phase M-channel filter banks and wavelets, including a comprehensive theory of permissible lengths, minimal structures for parametrization and fast computation, and mappings for two-dimensional signal processing. Criteria for wavelet filter design are also being addressed, including vanishing moments, smoothness and nonnegativity of the scaling function, and unequal length filters. The investigators are studying applications of the above to perceptually-based data compression of image, video and seismic data, multicarrier modulation, and multiscale feature detections. They are also investigating the use of the M-band wavelet transform for multitone modulation. The frequency partitioning properties of the M-channel filter bank enable high efficiency for channels such as twisted-pair copper wire and hybrid fiber-coax, with reduced susceptibility to narrow-band interference.