Multivariate Wavelet Analysis: Constructions and Specific Applications

本课题主要研究小波的构造及其应用。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。使用一般的比例尺有一些主要的优点。这个项目的一个目的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所浪费。因此，我们要开发的建设原则，以经济的方式产生合适的小波/多小波基。我们将集中在小波与一些额外的功能，如某些插值属性。此外，我们打算调查，如果一般的缩放矩阵可以从信号/图像分析的某些应用程序中，特别是关于一般类型的噪声去噪算法是有帮助的。分析将伴随着高效的数据结构，这是适应小波算法的具体要求的发展。

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.