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从压缩传感到低秩矩阵恢复: 理论与应用

彭义刚 索津莉 戴琼海 徐文立

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. 自动化学报, 2013, 39(7): 981-994. doi: 10.3724/SP.J.1004.2013.00981
引用本文: 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. 自动化学报, 2013, 39(7): 981-994. doi: 10.3724/SP.J.1004.2013.00981
PENG Yi-Gang, SUO Jin-Li, DAI Qiong-Hai, XU Wen-Li. From Compressed Sensing to Low-rank Matrix Recovery: Theory and Applications. ACTA AUTOMATICA SINICA, 2013, 39(7): 981-994. doi: 10.3724/SP.J.1004.2013.00981
Citation: PENG Yi-Gang, SUO Jin-Li, DAI Qiong-Hai, XU Wen-Li. From Compressed Sensing to Low-rank Matrix Recovery: Theory and Applications. ACTA AUTOMATICA SINICA, 2013, 39(7): 981-994. 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

doi: 10.3724/SP.J.1004.2013.00981
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

详细信息
    通讯作者:

    彭义刚

From Compressed Sensing to Low-rank Matrix Recovery: Theory and Applications

Funds: 

Supported by National Basic Research Program of China (973 Program) (2010CB731800) and National Natural Science Foundation of China (61035002, 61171119)

  • 摘要: 综述了压缩传感、矩阵秩最小化和低秩矩阵恢复等方面的基础理论及典型应用. 基于凸优化的压缩传感及由其衍生的矩阵秩最小化和低秩矩阵恢复是近年来的研究热点,在信号处理、 推荐系统、高维数据分析、图像处理、计算机视觉等很多研究领域具有重要和成功的应用. 在这些实际的应用中,往往涉及到对高维数据的分析与处理,需要充分和合理利用数据中的如稀疏性或其所构成矩阵的低秩性等性质. 尽管在最坏情况下,最小化诸如稀疏性或矩阵秩这样的目标函数是 NP 难的,但是在某些合理的假设条件下,通过优化目标函数的凸松弛替代函数, 采用凸优化的方法,能够精确地给出原问题的最优解. 有很多高效的凸优化算法对之进行求解且适用于大规模问题.本文首先分别综述了压缩传感、 矩阵秩最小化和低秩矩阵恢复的相关基础理论,然后对其在图像处理、计算机视觉和计算摄像学等领域的典型应用予以举例介绍,并展望了相关领域未来的研究工作.
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  • 收稿日期:  2012-02-20
  • 修回日期:  2012-10-31
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