Theory and Algorithms for Exploiting Sparsity in Signal Processing Applications

在信号处理应用中利用稀疏性的理论和算法

• 批准号: 0830612
• 负责人: Bhaskar Rao
• 金额: $ 53.61万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-15 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0830612&HistoricalAwards=false
• 关键词: Theory; Algorithms; Exploiting; Sparsity; Signal

AbstractThis research examines theoretical, algorithmic, and computational issues that arise in signal processing problems where there is a need to compute sparse solutions. There are numerous signal-processing applications where sparsity constraint on the solution vector naturally arises. Brain imaging techniques such as MEG and EEG, sparse communication channels with large delay spread, high-resolution spectral analysis, direction of arrival estimation and compressed sensing are a few examples. The generalization and extension of the sparse Bayesian learning (SBL) techniques considered in this research will broaden the application domain and provide a very powerful complement to the existing maximum a posteriori (MAP) methods commonly used and in some cases even surpass them.The investigators study extensions and generalizations of the sparse source recovery problem to greatly broaden the application domain. A key consideration in the work is developing a rigorous framework to deal with dependency in the sparsity framework. Motivated by applications with sparse but local structure, the research considers intra-vector dependency in the single measurement case, as well as intra-vector dependency as required in the multiple measurement contexts, among others. The research also includes the development of connections between multi-user communication theory and the sparse signal recovery problem to shed light on the stability with which sparse signal recovery is possible and to develop an understanding of the limits of suboptimal source recovery methods. To deal with non-stationary environments, the research develops on-line adaptive algorithms that exploit the inherent sparse structure of the application. The research also includes evaluation of the resulting algorithms in several important application domains.Level of Effort StatementAt the recommended level of support, the PI and co-PI will make every attempt to meet the original scope and level of effort of the project.

摘要这项研究研究了在需要计算稀疏解决方案的信号处理问题中出现的理论，算法和计算问题。有许多信号处理应用程序，其中稀疏性限制自然会产生溶液向量。大脑成像技术，例如MEG和EEG，稀疏延迟扩散，高分辨率光谱分析，到达估计方向和压缩感应的稀疏通信通道就是一些例子。本研究中考虑的稀疏贝叶斯学习（SBL）技术的概括和扩展将扩大应用领域，并为现有最大值A后验（MAP）方法提供非常有力的补充，在某些情况下甚至超过了它们。工作中的一个关键考虑是开发一个严格的框架来处理稀疏框架中的依赖性。由稀疏但局部结构的应用激发，该研究考虑了单个测量案例中的向量依赖性，以及在多个测量环境中所需的媒介内依赖性等。该研究还包括多用户通信理论与稀疏信号恢复问题之间的连接发展，以阐明稀疏信号恢复的稳定性，并了解次优源恢复方法的限制。为了处理非平稳环境，研究开发了在线自适应算法，以利用应用程序的固有结构。该研究还包括评估几个重要应用程序域中所得算法的评估。