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基于l1-l2范数的块稀疏信号重构

陈鹏清 黄尉

陈鹏清, 黄尉. 基于l1-l2范数的块稀疏信号重构[J]. 应用数学和力学, 2017, 38(8): 932-942. doi: 10.21656/1000-0887.370230
引用本文: 陈鹏清, 黄尉. 基于l1-l2范数的块稀疏信号重构[J]. 应用数学和力学, 2017, 38(8): 932-942. doi: 10.21656/1000-0887.370230
CHEN Peng-qing, HUANG Wei. Block-Sparse Signal Recovery Based on l1-l2 Norm Minimization[J]. Applied Mathematics and Mechanics, 2017, 38(8): 932-942. doi: 10.21656/1000-0887.370230
Citation: CHEN Peng-qing, HUANG Wei. Block-Sparse Signal Recovery Based on l1-l2 Norm Minimization[J]. Applied Mathematics and Mechanics, 2017, 38(8): 932-942. doi: 10.21656/1000-0887.370230

基于l1-l2范数的块稀疏信号重构

doi: 10.21656/1000-0887.370230
基金项目: 国家自然科学基金重大研究计划(91538112);国家自然科学基金青年科学基金(11201450)
详细信息
    作者简介:

    陈鹏清(1991—),男,硕士生(E-mail: pqchen5@163.com);黄尉(1977—),男,博士,硕士生导师(通讯作者. E-mail: whuang@hfut.edu.cn).

  • 中图分类号: O174.2

Block-Sparse Signal Recovery Based on l1-l2 Norm Minimization

Funds: The Major Research Plan of the National Natural Science Foundation of China(91538112);The National Science Fund for Young Scholars of China(11201450)
  • 摘要: 压缩感知(compressed sensing,CS) 是一种全新的信息采集与处理的理论框架,借助信号内在的稀疏性或可压缩性,可以从小规模的线性、非自适应的测量中通过求解非线性优化问题重构原信号.块稀疏信号是一种具有块结构的信号,即信号的非零元是成块出现的.受YIN Peng-hang, LOU Yi-fei, HE Qi等提出的l1-2范数最小化方法的启发,将基于l1-l2范数的稀疏重构算法推广到块稀疏模型,证明了块稀疏模型下l1-l2范数的相关性质,建立了基于l1-l2范数的块稀疏信号精确重构的充分条件,并通过DCA(difference of convex functions algorithm) 和ADMM(alternating direction method of multipliers)给出了求解块稀疏模型下l1-l2范数的迭代方法.数值实验表明,基于l1-l2范数的块稀疏重构算法比其他块稀疏重构算法具有更高的重构成功率.
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出版历程
  • 收稿日期:  2016-07-22
  • 修回日期:  2017-05-19
  • 刊出日期:  2017-08-15

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