任意维CDF97型滤波器组的格型结构设计研究

Lattice structure is very efficient for the design and implementation of filter banks. It is able to structurally provide filter banks with several kinds of practical properties, and can also implement filter banks using quick and robust circuits. Nowadays, the investigations of lattice structure are mainly devoted to filter banks of which the included filters have equal length and identical center. In contrast, the research is limited to special one-dimensional cases as to filter banks with the included filters having unequal lengths and different centers, though such filter banks are more proper for practical applications. The latter kind of filter banks includes the famous CDF97 filter bank as a special case, and therefore can be named as type-CDF97 filter banks. The proposal is devoted to the lattice structure for arbitrary dimensional type-CDF97 filter banks. The designed type-CDF97 filter banks will structurally satisfy several kinds of properties such as linear phase and perfect reconstruction. The design will cover both one-dimensional and multi-dimensional cases, both critically sampled and oversampled cases, and both integral length and arbitrary length cases. In addition, we will investigate the optimization of type-CDF97 filter banks yielded by lattice structure. The involved free parameters will be adjusted to produce more practical filter banks. The optimized type-CDF97 filter banks will be used in several kinds of signal processing problems, and filter banks choices and applications rules will be established regarding specific problems.

格型结构在滤波器组的设计和实现上非常有效，它不仅能使滤波器组结构性满足多种实用性质，而且提供快速鲁棒的电路实现。目前格型结构的滤波器组设计成果，多为“各滤波器长度相等、中心相同”的特殊滤波器组，而应用前景更广的“各滤波器长度不等、中心不同”的滤波器组研究仅限一维的极个别情形。后者包含著名的CDF97滤波器组为特例，不妨称之为CDF97型滤波器组。本项目拟开展任意维CDF97型滤波器组的格型结构设计研究，所设计的CDF97型滤波器组，将结构性满足线性相位与完全重构等多种性质，并且兼顾一维与多维情形，囊括严格采样与过采样情形，包罗整数长度与任意长度情形。此外，我们将探讨CDF97型滤波器组的格型结构优化问题，通过调整格型结构包含的自由参数以设计更为实用的滤波器组，将优化所得CDF97型滤波器组应用于多种信号处理问题，寻求建立与具体问题相结合的滤波器组选用与应用规则。

格型结构在滤波器组的设计上非常有效。本项目主要研究滤波器组的格型结构，相关结果包括滤波器理论与滤波器应用。在滤波器理论方面，项目组总结了自己的滤波器研究结果，获得了湖南省自然科学三等奖一项；项目组描述了自己的滤波器格型结构设计及相应自由参数初始化结果，撰写了格型结构专著一部（准备出版）。在滤波器应用方面，项目组将滤波器应用到目标跟踪、CT脑图像分割、视网膜图像分割等问题，取得了较好的应用效果，相应结果发表在《IET Image Processing》、《IEEE Transactions on Instrumentation and Measurement》等期刊。项目组共完成自然科学奖励一项、SCI期刊论文7篇。