自动化学报2013，Vol.39Issue(7)：981-994,14.DOI:10.3724/SP.J.1004.2013.00981
从压缩传感到低秩矩阵恢复:理论与应用
From Compressed Sensing to Low-rank Matrix Recovery:Theory and Applications
摘要
Abstract
This paper reviews the basic theory and typical applications of compressed sensing,matrix rank minimization,and low-rank matrix recovery.Compressed sensing based on convex optimization and related matrix rank minimization and low-rank matrix recovery are hot research topics in recent years.They find many important and successful applications in different research fields,including signal processing,recommending system,high-dimensional data analysis,image processing,computer vision and many others.In these real applications,analysis and processing of high-dimensional data are often involved,which needs to utilize the structure of data,such as sparsity or low rank property of the data matrix,sufficiently and reasonably.Although minimization of objective functions like sparsity or matrix rank is NP-hard in the worst case,by optimizing the convex relaxation of the original objective function under certain reasonable assumptions,convex optimization could give the optimal solution of the original problem.Moreover,many efficient convex optimization algorithms could be used for solving the problem and are also applicable to large-scale problems.In this paper,we first review the fundamental theories about compressed sensing,matrix rank minimization,and low-rank matrix recovery.Then,we introduce the typical applications of these theories in image processing,computer vision,and computational photography.We also look into the future work in related research areas.关键词
压缩传感/矩阵秩最小化/低秩矩阵恢复/凸优化Key words
Compressed sensing/matrix rank minimization/low-rank matrix recovery/convex optimization引用本文复制引用
彭义刚,索津莉,戴琼海,徐文立..从压缩传感到低秩矩阵恢复:理论与应用[J].自动化学报,2013,39(7):981-994,14.基金项目
国家重点基础研究发展计划(973计划)(2010CB731800),国家自然科学基金(61035002,61171119)资助 （973计划）
Supported by National Basic Research Program of China (973 Program)(2010CB731800) and National Natural Science Foundation of China (61035002,61171119) （973 Program）
