Multidimensional wavelets in non-isotropic function spaces

非各向同性函数空间中的多维小波

基本信息

批准号：
0653881
负责人：
Marcin Bownik
金额：
$ 11.96万
依托单位：
University of Oregon Eugene
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2007
资助国家：
美国
起止时间：
2007-07-01 至 2010-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0653881&HistoricalAwards=false
关键词：
Multidimensional wavelets non isotropic function

项目摘要

The project involves education and research activities in harmonic analysis concerning the mathematical theory of multi-dimensional wavelet expansions. One of the fundamental problems of the subject is how to construct wavelets with desired properties such as good time-frequency localization. Despite significant progress in this area, the majority of research has been concentrated on isotropic theory andnon-isotropic wavelet theory lags far behind. One of the main research directions of the project is the development of techniques for construction of well-localized orthogonal wavelets for large classesof non-isotropic expansive dilations. A closely related complementary topic is the identification of non-isotropic dilations for which the construction of well-localized wavelets is not possible.Another direction of the project is to study non-isotropic analogues of classical function spaces associated to expansive dilations. More generally, the project represents work on wavelet analysis which is a powerful technique in harmonic analysis. Non-isotropic wavelet theory in higher dimensions has a potential for wide applications both in pure analysis and more applied areas of signal and image processing comparable to that of already well established isotropic wavelet theory. The main goal of the project is to integrate research and education activities in the multidimensional wavelet theory which could make further applications of non-isotropic wavelets possible.

该项目涉及有关多维小波扩展的数学理论的谐波分析中的教育和研究活动。该主题的基本问题之一是如何构建具有所需属性（例如良好时频定位）的小波。尽管在这一领域取得了重大进展，但大多数研究集中在各向同性理论上，而non-disotropic小波理论却远远落后。该项目的主要研究方向之一是开发用于构建非各向异性扩张扩张大型类正交的正交小波的技术。一个密切相关的互补话题是鉴定非各向异性扩张，无法为其构建良好的小波构建。更一般而言，该项目代表了小波分析的工作，这是谐波分析中的一种强大技术。在较高维度中，非各向异性小波理论具有在纯分析和更广泛的信号和图像处理领域的广泛应用，与已经建立的各向同性小波理论相当。该项目的主要目标是将研究和教育活动整合到多维小波理论中，这可以使非异端小波的进一步应用成为可能。