Theory, Algorithms, and Applications of Signal Processing with the Sparseness Constraint

稀疏约束信号处理的理论、算法和应用

• 批准号: 9902961
• 负责人: Bhaskar Rao
• 金额: $ 29.92万
• 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: 1999
• 资助国家: 美国
• 起止时间: 1999-07-01 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9902961&HistoricalAwards=false
• 关键词: Theory; Algorithms; Applications; Signal; Processing

CCR-9902961RaoTHEORY, ALGORITHMS, AND APPLICATIONS OF SIGNAL PROCESSING WITH THE SPARSENESS CONSTRAINT This research project will examine the theoretical and computational issues that arise in signal processing problems with the sparseness constraint in several important application domains. The research plan includes using majorization theory to develop and identify suitable diversity measures whose minimization leads to sparse solutions. Then, to minimize these measures, a new class of optimization algorithms will be developed, analyzed, and applied. Algorithms based on a factored representation for the gradient along with Affine Scaling Transformation (AST) based methods of interior point optimization theory will be the starting point of this work. To facilitate a more comprehensive understanding of the methods, and to develop methods robust to noise, a Bayesian framework will be employed. The important extension to the multiple measurement vector problem will be studied greatly expanding the range of applications. Learning algorithms will be developed to tune the required overcomplete dictionaries for specific application environments, thereby increasing their overall effectiveness. Theoretical and algorithmic development will be guided by the requirements of the applications. Particular attention will be given to the applications of signal representation and neuromagnetic imaging using Magnetoencephalography (MEG) (a potentially important new modality for the imaging of the brain).

CCR-9902961Rao 稀疏约束信号处理的理论、算法和应用 该研究项目将研究几个重要应用领域中稀疏约束信号处理问题中出现的理论和计算问题。研究计划包括使用多数化理论来开发和确定合适的多样性措施，其最小化会导致稀疏解决方案。然后，为了最大限度地减少这些措施，将开发、分析和应用一类新的优化算法。基于梯度分解表示的算法以及基于仿射缩放变换 (AST) 的内点优化理论方法将是这项工作的起点。为了促进对这些方法的更全面的理解，并开发对噪声具有鲁棒性的方法，将采用贝叶斯框架。将研究多测量向量问题的重要扩展，极大地扩展应用范围。将开发学习算法来调整特定应用环境所需的超完备词典，从而提高其整体有效性。理论和算法的开发将以应用的要求为指导。将特别关注使用脑磁图（MEG）（一种潜在重要的大脑成像新模式）进行信号表示和神经磁成像的应用。