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

复值信号处理及其在脑成像数据分析中的应用

• 批准号: 0840895
• 负责人: Vince Calhoun
• 金额: $ 15.02万
• 依托单位: The MIND Research Network
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0840895&HistoricalAwards=false
• 关键词: Complex; Valued; Signal; Processing; its

Collaborative Research: Complex-Valued Signal Processing and its Application to Analysis of Brain Imaging Data Complex-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：复值信号处理及其在脑成像数据分析中的应用复值信号经常出现在通信、雷达和生物医学等多种应用中，因为大多数实用的调制格式都是复杂类型，并且在雷达和生物医学等应用中也经常出现。磁共振成像产生的数据本质上是复杂的。复数域不仅为这些信号提供了方便的表示，而且还提供了一种保留信号的物理特性及其所经历的变换的自然方式。然而，复杂域在信号处理算法的推导和分析方面也提出了许多挑战，因此，为复杂域开发的绝大多数算法都采取了限制其实用性的捷径。这项研究建立了复值信号处理的框架，以便能够充分发挥复值信号处理的潜力。它允许在复杂域中进行所有计算，从而无需在算法的推导和分析中进行许多简化假设，例如信号的循环性。它还允许使用完全复杂的函数，而不是更常用的有界但非分析函数。这些函数通过有效生成高阶统计信息，为执行独立成分分析 (ICA) 提供了有吸引力的替代方案。使用该框架，衍生出一类新的高效算法，用于在复杂领域执行 ICA，特别是使用原始复杂形式的医学成像数据来研究大脑功能。