Fast Computational Methods and Subspace Algebra in Signal Processing Algorithms and Implementations

本项目的研究活动将利用线性矩阵代数的概念来设计用于信号处理的快速计算算法。在过去的十年中，线性矩阵代数的概念在信号处理算法的发展中占据了中心地位。许多实际信号处理问题的解都可以用矩阵的秩和相应的子空间来表示。事实上，子空间在信号处理中的重要性是开发子空间代数工具的动力，即多线性代数。线性和多元线性代数的一些重要应用领域包括到达方向估计、频率估计、信号检测、地震和地质勘探、结构动力分析、生物医学信号处理、系统识别、化学和经济学。

The research activity in this project will utilize concepts of linear matrix algebra to design fast computational algorithms for signal processing. In the last decade, concepts from linear matrix algebra have acquired a central position in the development of signal processing algorithms. The solution to many practical signal processing problems can be obtained in terms of ranks of certain matrices and corresponding subspaces. In fact, the importance of subspaces in signal processing is motivation for developing tools from the algebra of subspaces, multilinear algebra. Some important application areas for linear and multilinear algebra include direction of arrival estimation, frequency estimation, signal detection, seismic and geological exploration, dynamic analysis of structures, biomedical signal processing, system identification, chemistry and economics.