Multivariate Wavelet Analysis: Constructions and Specific Applications

多元小波分析：结构和具体应用

• 批准号: 5334062
• 负责人: Professor Dr. Stephan Dahlke
• 金额: --
• 依托单位: Arbeitsgruppe Numerik (Dahlke)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2001
• 资助国家: 德国
• 起止时间: 2000-12-31 至 2007-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5334062?language=en
• 关键词: Multivariate; Wavelet; Analysis; Constructions; Specific

This project is concerned with the construction and the applications of wavelets. We are especially interested in nonseparable multivariate wavelets with respect to general scaling matrices. The use of general scalings provides some principal advantages. One aim of this project is to investigate if these superiorities really count when it comes to practical applications, or if they are wasted by an overhead of technical difficulties. We therefore want to develop construction principles which yield suitable wavelet/multiwavelet bases in an economical way. We shall focus on wavelets with some additional features such as certain interpolation properties. Furthermore, we intend to investigate if general scaling matrices can be helpful in certain applications from signal/image analysis, especially concerning denoising algorithms for general kinds of noise. The analysis will be accompanied by the development of efficient data structures which are adapted to the specific requirements of wavelet algorithms.

本课题主要研究小波的构造和应用。我们特别感兴趣的是关于一般尺度矩阵的不可分多元小波。使用常规缩放提供了一些主要优势。这个项目的一个目标是调查这些优势在实际应用中是否真的重要，或者它们是否被技术困难的开销所浪费。因此，我们希望开发能够以经济的方式产生合适的小波/多小波基的构造原理。我们将重点介绍具有某些附加特征的小波，例如某些内插性质。此外，我们打算研究一般的尺度矩阵在信号/图像分析的某些应用中是否有帮助，特别是对于一般类型的噪声的去噪算法。在进行分析的同时，还将开发出适应小波算法特定要求的高效数据结构。