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.

该项目涉及小波的构建和应用。对于一般缩放矩阵，我们对不可分割的多元小波特别感兴趣。通用量表的使用提供了一些主要优势。该项目的目的之一是调查这些优势在实际应用方面是否真的很重要，还是由于技术困难的开销而浪费了这些优势。因此，我们希望制定建筑原则，以经济的方式产生合适的小波/多波网基础。我们将专注于具有一些其他特征的小波，例如某些插值特性。此外，我们打算调查一般缩放矩阵是否对信号/图像分析中的某些应用有帮助，尤其是关于对一般噪声的授权算法的范围。该分析将伴随着有效的数据结构的发展，这些数据结构适合小波算法的特定要求。