An interdisciplinary evaluation of mathematical methods in signal and image processing

这个DFG-Schwerpunktprogramm的总体目标是发展信号和图像处理中应用的数学方法。科学的重点是从多尺度分析，非线性动力学和统计方法。除了不同项目的具体研究，这将或多或少地在每个科学学科的范围内进行，对这些不同方法进行严格的跨学科评估对于proram的成功至关重要。这将在本项目中完成。首先，这需要一个具有典型测试示例（医学和/或地球物理/环境应用）的数据池。在对这些方法进行评估之前，必须将不同的方法统一并整合到一个软件工具箱中。此外，评价过程需要普遍接受的标准，这将与特定用户，即医学科学家、地球科学家合作制定。此外，本计画也将探讨小波分析所产生的一个问题。从真实的应用中获得的数据是通过测量仪器获得的，这些测量仪器将原始数据f.在最简单的情况下，测量特性由卷积算子描述。更一般地，测量过程通常可以用紧致算子A来建模。在这个项目中，小波变换的可用数据Af和相关的指标函数，这将允许所需的结论f本身，将被构造和分析。

The overall aim of this DFG-Schwerpunktprogramm is the development of mathematical methods for applications in signal and image processing. The scientific focus is on methods from multiscale analysis, non-linear dynamics and statistics. Besides the specific research of the different projects, which will be done more or less within the scope of each scientific discipline, a strict and interdisciplinary evaluation of these different methods is of high importance for the success of the proram. This will be done in this project. First of all, this requires a data pool with typical test examples (medical and/or geophysical/enviromental applications). The different methods have to be homogenized and integrated into a software toolbox before an evaluation of these methods can be carried out. Moreover, commonly accepted criteria are necessary for the evaluation process, this will be worked out in cooperation with specific users, i.e. medical scientists, geoscientists. In addition, a problem arising from wavelet analysis will be investigated in this project. Data from real applications are obtained by measuring instruments, which transform the original data f. In the simplest case the measurement characteristic is described by convolution operators. More general, the measurement process can often be modelled by compact operators A. In this project, wavelet transforms of the available data Af and related indicator functions, which will allow the desired conlusions on f itself, will be constructed and analyzed.