An interdisciplinary evaluation of mathematical methods in signal and image processing

信号和图像处理中数学方法的跨学科评估

• 批准号: 5334144
• 负责人: Professor Dr. Peter Maaß
• 金额: --
• 依托单位: Zentrum für Technomathematik (ZeTeM)
• 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 2005-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5334144?language=en
• 关键词: interdisciplinary; evaluation; mathematical; methods; signal

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.

该 DFG-Schwerpunkt 计划的总体目标是开发信号和图像处理应用的数学方法。科学重点是多尺度分析、非线性动力学和统计学方法。除了不同项目的具体研究之外，这些研究或多或少将在每个科学学科的范围内进行，对这些不同方法的严格和跨学科评估对于该项目的成功非常重要。这将在这个项目中完成。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，必须将不同的方法同质化并集成到软件工具箱中。此外，评估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，本项目还将研究小波分析产生的问题。实际应用的数据是通过测量仪器获得的，测量仪器将原始数据f转换。在最简单的情况下，测量特性由卷积算子描述。更一般地，测量过程通常可以通过紧凑算子 A 来建模。在该项目中，将构建和分析可用数据 Af 和相关指示函数的小波变换，这将允许对 f 本身得出所需的结论。