低秩矩阵近似与优化问题研究进展

摘要

Based on the compression and recovery of high-dimensional data, the development process from the theory of Shannon sampling to sparse representation and compression perception and then to low-rank matrix problem is described. Then, the importance of low rank matrix relaxation and optimization problem is discussed. Subsequently, a detailed review of the existing methods is introduced from three aspects of low rank matrix minimization, decomposition, optimization and applications. Finally, some reasonable suggestions on the deficiencies of current research and the future research direction are put forward.%首先以高维数据压缩与恢复为背景,详细阐述由香农采样理论到稀疏表示和压缩感知理论再到低秩矩阵问题的发展历程,引出低秩矩阵近似与优化问题的重要性.然后,从低秩矩阵最小化问题、低秩矩阵分解问题、低秩矩阵的优化与应用三方面对现有方法进行详细的综述.最后对当前研究的不足之处与未来的研究方向提出合理的建议.