Collaborative Research: Complex-Valued Signal Processing and its Application to Analysis of Brain Imaging Data

合作研究：复值信号处理及其在脑成像数据分析中的应用

• 批准号: 0635129
• 负责人: Tulay Adali
• 金额: --
• 依托单位: University of Maryland Baltimore County
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-15 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0635129&HistoricalAwards=false
• 关键词: Collaborative; Research; Complex; Valued; Signal

Collaborative Research: Complex-Valued Signal Processing and its Application to Analysis of Brain Imaging DataComplex-valued signals arise frequently in applications as diverse as communications, radar, and biomedicine, as most practical modulation formats are of complex type and applications such as radar and magnetic resonance imaging lead to data that are inherently complex valued. The complex domain not only provides a convenient representation for these signals but also a natural way to preserve the physical characteristics of the signals and the transformations they go though. The complex domain, however, also presents a number of challenges in the derivation and analysis of signal processing algorithms, and as a result, the vast majority of algorithms developed for the complex domain have taken shortcuts limiting their usefulness.This research establishes a framework for complex-valued signal processing such that the full potential of complex-valued signal processing can be realized. It allows for all computations to be carried out in the complex domain eliminating the need for many simplifying assumptions, such as the circularity of signal, both in the derivation and the analysis of the algorithms. It also allows for the use of fully complex functions rather than the more commonly utilized bounded but non-analytic functions. These functions provide attractive alternatives for performing independent component analysis(ICA) by efficiently generating higher-order statistical information. Using this framework, a new class of efficient algorithms are derived for performing ICA in the complex domain, in particular, for studying brain function using the medical imaging data in its native, complex form.

协作研究：复杂价值的信号处理及其在分析脑成像数据杂志可值下的信号中的应用在像通信，雷达和生物医学等应用中经常出现，因为大多数实用的调制格式都是复杂的类型，以及诸如雷达和磁性共振成像之类的应用程序类型，导致具有内在复杂价值的数据。复杂的域不仅为这些信号提供了方便的表示，而且还提供了一种自然的方式来保留信号的物理特征及其所进行的转换。然而，复杂的领域在信号处理算法的推导和分析中也提出了许多挑战，结果，为复杂领域开发的绝大多数算法都采用了捷径限制了它们的实用性。这项研究建立了一个用于复杂的信号处理的框架，以使其具有复杂信号的全部潜在的复杂信号处理，可以实现复杂的信号处理。它允许在复杂域中进行所有计算，从而消除了对许多简化假设的需求，例如信号的循环，无论是在算法的推导和分析中。它还允许使用完全复杂的功能，而不是更常用的有限但非分析功能。这些功能通过有效生成高阶统计信息为执行独立组件分析（ICA）提供了有吸引力的替代方案。 使用此框架，将得出了一种新的有效算法，用于在复杂域中执行ICA，特别是用于使用其天然，复杂形式的医学成像数据研究大脑功能。