Data, Signal, and Image Modeling: Theory and Algorithms

数据、信号和图像建模：理论和算法

• 批准号: 0504788
• 负责人: Akram Aldroubi
• 金额: --
• 依托单位: Vanderbilt University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-08-01 至 2009-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0504788&HistoricalAwards=false
• 关键词: Data; Signal; Image; Modeling; Theory

To analyze and process signals, or images, a mathematical signal model is first chosen to describe the data. For example, band limited or spline models are often used for the acquisition of Diffusion Tensor Magnetic Resonance Images (DTMRI) and for tracking white matter in the brain. Sampling, data compression, or data transmission are often modeled by shift-invariant spaces such as wavelets. The goals of this research include the development of a mathematical framework for finding the "best" shift-invariant model from observed data for a given class of signals, and the development of computationally efficient algorithms for finding the so-called shift-invariant signal models.For many applications, it is important to adapt the signal model to the observed data in order to improve the quality of the analysis, or to reduce the processing time, for example. To find the shift-invariant space model that is optimally adapted to a given class of measured data, this project will develop mathematical transformations that render the search mathematically and computationally manageable. Testing and applications will focus on Diffusion Tensor Magnetic Resonance images, and data obtained from mass spectrometry for visualizing the location of proteins in tissues.

为了分析和处理信号或图像，首先选择数学信号模型来描述数据。 例如，频带受限或样条模型通常用于采集扩散张量磁共振图像（DTMRI）和用于跟踪大脑中的白色物质。 采样、数据压缩或数据传输通常由移位不变空间（如小波）建模。 本研究的目标包括发展一个数学框架，用于从给定类别的信号的观测数据中找到“最佳”移不变模型，以及发展计算效率高的算法，用于找到所谓的移不变信号模型。对于许多应用，重要的是使信号模型适应观测数据，以提高分析的质量，或者例如减少处理时间。 为了找到最适合给定类别测量数据的平移不变空间模型，该项目将开发数学变换，使搜索在数学和计算上易于管理。 测试和应用将集中在扩散张量磁共振图像，以及从质谱法获得的数据，用于可视化组织中蛋白质的位置。