多元二代小波构造及其自适应选择机制研究

项目名称： 多元二代小波构造及其自适应选择机制研究

项目编号： No.61202192

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 计算机科学学科

项目作者： 肖芬

作者单位： 湘潭大学

项目金额： 24万元

中文摘要： 高维数据处理已成为当前小波研究领域所面临的一大挑战，构造具有各种重要性质的多元小波是其成功应用的关键保障。提升格式是构造第二代小波、实现自适应小波变换最为有效的方法之一。为了满足不同应用的需要，本项目拟开展第二代多元小波的设计及其在图像处理中的自适应机制研究,重点研究各类多元小波的对称、消失矩、紧支、插值等重要性质与提升算子之间的关系，建立满足各种重要性质的多元二代小波一般性构造算法；同时将构造得到的小波应用于图像处理，研究多元小波的对称性、消失矩阶数、支撑长度对不同应用图像的影响，设计一种基于图像特征的小波自适应选取方案，为多元小波在图像处理中的实际应用提供科学设计指南。本研究对完善小波分析理论、推动小波在高维信号处理和大规模科学计算等领域的应用具有重要的理论价值。

中文关键词： 提升格式；多元小波；滤波器；图像处理；生物信息处理

英文摘要： Wavelet analysis is a powerful tool in signal processing. Most of its application fields are in the case of high dimensions. One of the challenging problems in wavelets is the high-dimensional data analysis. Construction of multivariate wavelet systems with good properties is the key issue to the success of its application. The lifting scheme is a new technique for both designing wavelets and performing the adaptive wavelet transform. The resulted wavelet is referred as the second generation wavelet. According to the entirely spatial-domain interpretation, it worthwhile to simplify the multivariate wavelet construction to some extent. In this work, based on the lifting scheme, we will focus on the multidimensional wavelets construction and its adaptive selection schemes for image processing. Multivariate wavelets include 2-band wavelets, multiband wavelets, scalar wavelets, multiwavelets and their corresponding prefilters all will be concerned in this work. The relationships between the lifting operators and the important properties of wavelets, such as the symmetry, vanishing moment, compact support and interpolation, will also be systematically studied. The proposal aims to achieve a general framework for constructing multivariate wavelet with the given desired properties. According to some properties such as

英文关键词： Lifting scheme；Multivariate wavelet；Filter bank；Image processing；biological information processing