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静态图像压缩的新一代标准。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。本研究探讨正交和双正交线性相位m通道滤波器组和m波段对称小波的理论、设计和应用。多速率滤波器组是子带和小波分解以及频域/时域复用的基本组成部分。该研究解决的理论问题包括线性相位m通道滤波器组和小波的结构，包括允许长度的综合理论，参数化和快速计算的最小结构，以及二维信号处理的映射。小波滤波器设计的准则也得到了解决，包括消失矩，平滑性和缩放函数的非负性，以及不等长滤波器。研究人员正在研究上述技术在基于感知的图像、视频和地震数据压缩、多载波调制和多尺度特征检测方面的应用。他们也在研究m波段小波变换在多音调制中的应用。m通道滤波器组的频分特性使双绞线铜线和混合光纤同轴电缆等通道具有高效率，同时降低了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.