Wavelet- and Frame-based treatments of variational problems with applications in geophysical data processing (in particular ocean margin analysis)

信号处理中的大多数应用，例如测量生产过程或分析气象数据(气压、风速等)，都需要对相关系统参数进行定量估计。连续小波方法在这一领域的成功取决于对基本小波的优化选择和用于评估所得到的小波变换的适当工具。本项目的主要目的是研究基于不同优化准则(局部化、测不准原理、再生核、扩散方程)的一维和多维小波的构造原理。相关的连续小波变换将用于研究真实的大气数据(与Deutscher Wetterdienst，Lindenberg和Pompe博士，Greifswald合作)。实际生活中的数据受到测量噪声的污染，通常没有正确地将其建模为白噪声。因此，优化的处理方法需要分析潜在的随机噪声模型(合作教授Franke，Kaiserslautern)。

Most applications in signal processing, e.g. surveying production processes or analyzing meteorological data (air pressure, wind speed, etc.), require quantitative estimates of the relevant system parameters. The success of continuous wavelet methods in this field depends on an optimized choice of the basic wavelet and on adapted tools for evaluating the resulting wavelet transform. The main aim of this project is the investigation of construction principles for 1D and multidimensional wavelets, which are based on different optimization criteria (localization, uncertainty principles, reproducing kernels, diffusion equations). The related continuous wavelet transform will be used to investigate real atmospheric data (cooperation with Deutscher Wetterdienst, Lindenberg and Dr. Pompe, Greifswald). Real life data are contaminated by measurement noise, usually this is not properly modeled as white noise. Optimized processing methods therefore require to analyze the underlying stochastic noise model (cooperation Prof. Franke, Kaiserslautern).