Multivariate Wavelet Analysis: Constructions and Specific Applications

点击翻译按钮获取中文摘要

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.