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基于l2/lq(q=2/3)最小化模型的块稀疏信号恢复

祝德春 周珺 曹满霞 黄尉

祝德春, 周珺, 曹满霞, 黄尉. 基于l2/lq(q=2/3)最小化模型的块稀疏信号恢复[J]. 应用数学和力学, 2021, 42(9): 989-998. doi: 10.21656/1000-0887.420009
引用本文: 祝德春, 周珺, 曹满霞, 黄尉. 基于l2/lq(q=2/3)最小化模型的块稀疏信号恢复[J]. 应用数学和力学, 2021, 42(9): 989-998. doi: 10.21656/1000-0887.420009
ZHU Dechun, ZHOU Jun, CAO Manxia, HUANG Wei. Block-Sparse Signal Recovery via l2/lq(q=2/3) Minimization[J]. Applied Mathematics and Mechanics, 2021, 42(9): 989-998. doi: 10.21656/1000-0887.420009
Citation: ZHU Dechun, ZHOU Jun, CAO Manxia, HUANG Wei. Block-Sparse Signal Recovery via l2/lq(q=2/3) Minimization[J]. Applied Mathematics and Mechanics, 2021, 42(9): 989-998. doi: 10.21656/1000-0887.420009

基于l2/lq(q=2/3)最小化模型的块稀疏信号恢复

doi: 10.21656/1000-0887.420009
基金项目: 

国家自然科学基金重大研究计划(91538112)

详细信息
    作者简介:

    祝德春(1996—),男,硕士生(E-mail: 2354544152@qq.com);周珺(1994—),女,硕士(E-mail: 1812253174@qq.com);曹满霞(1993—),女,硕士生(E-mail: caomx0809@163.com);黄尉(1977—),男,教授,博士,硕士生导师(通讯作者. E-mail: whuang@hfut.edu.cn).

    通讯作者:

    黄尉(1977—),男,教授,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 via l2/lq(q=2/3) Minimization

  • 摘要:

    该文主要研究了块稀疏信号的恢复问题.利用q块限制等距性质(0<q≤1),通过极小化混合l2/lq(q=2/3)范数,建立了块稀疏信号恢复的一个充分条件,并且得到了在有噪声情形下信号恢复的误差界.通过数值实验,验证了该模型对于块稀疏信号的恢复有较高的成功率.

  • HALDAR J, HERNANDO D, LIANG Z. Compressed-sensing MRI with random encoding[J].IEEE Transactions on Medical Imaging,2011,30(4): 893-903.
    [2]CANDES E J, TAO T. Decoding by linear programming[J].IEEE Transactions on Information Theory,2005, 51(12): 4203-4215.
    [3]PARVARESH F, VIKALO H, MISRA S, et al. Recovering sparse signals using sparse measurement matrices in compressed DNA microarrays[J].IEEE Journal of Selected Topics in Signal Processing,2008,2(3): 275-285.
    [4]MAIUMDAR A, WARD R. Compressed sensing of color images[J].Signal Processing,2010,90(12): 3122-3127.
    [5]VIDAL R, MA Y. A unified algebraic approach to 2-D and 3-D motion segmentation and estimation[J].Journal of Mathematical Imaging and Vision,2006, 25(3): 403-421.
    [6]LIN J, LI S. Block sparse recovery via mixed l2/l1 minimization[J].Acta Mathematica Sinica,2013,29(7): 1401-1412.
    [7]CHEN W, LI Y. The high order block RIP condition for signal recovery[J].Journal of Computational Mathematics,2019,37(1): 61-75.
    [8]HUANG J, WANG J, WANG W, et al. Sharp sufficient condition of block signal recovery via l2/l1-minimization[J].IET Signal Processing,2017,13(5): 495-505.
    [9]WANG Y, WANG J, XU Z. Restrictedp-isometry properties of nonconvex block-sparse compressed sensing[J].Signal Processing,2014,104: 188-196.
    [10]STOJNIC M, PARVARESH F, HASSIBI B. On the reconstruction of block-sparse signals with an optimal number of measurements[J].IEEE Transactions on Signal Processing,2009,57(8): 3075-3085.
    [11]ELDAR Y C, KUPPINGER P, BOLCSKEI H. Block-sparse signals: uncertainty relations and efficient recovery[J].IEEE Transactions on Signal Processing,2010,58(6): 3042-3054.
    [12]ELDAR Y C, MISHALI M. Robust recovery of signals from a structured union of subspaces[J].IEEE Transactions on Information Theory,2009,55(11): 5302-5316.
    [13]ZHOU S, KONG L, LUO Z, et al. New RIC bounds via lq-minimization with 0
    [14]DAVIES M E, GRIBONVAL R. Restricted isometry constants where lp sparse recovery can fail for 0
    [15]FOUCART S. A note on guaranteed sparse recovery via lp-minimization[J].Applied and Computational Harmonic Analysis,2010, 29(1): 97-103.
    [16]赵丹, 孙祥凯. 非凸多目标优化模型的一类鲁棒逼近最优性条件[J]. 应用数学和力学, 2019,40(6): 694-700.(ZHAO Dan, SUN Xiangkai. Some robust approximate optimality conditions for nonconvex multi-objective optimization problems[J].Applied Mathematics and Mechanics,2019,40(6): 694-700.(in Chinese))
    [17]王欣, 郭科. 一类非凸优化问题广义交替方向法的收敛性[J]. 应用数学和力学, 2018,39(12): 1410-1425.(WANG Xin, GUO Ke. Convergence of the generalized alternating direction method of multipliers for a class of nonconvex optimization problems[J].Applied Mathematics and Mechanics,2018,39(12): 1410-1425.(in Chinese))
    [18]DONOHO D L. Compressed sensing[J].IEEE Transactions on Information Theory,2006,52(4): 1289-1306.
    [19]CANDES E J, ROMBERG J, TAO T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information[J].IEEE Transactions on Information Theory,2006, 52(2): 489-509.
    [20]CANDES E J, WAKIN M B, BOYD S P. Enhancing sparsity by reweighted l1 minimization[J].Journal of Fourier Analysis and Applications,2008,14(5): 877-905.
    [21]NIE F P, WANG H, HUANG H, et al. Joint Schattenp-norm and lp-norm robust matrix completion for missing value recovery[J].Knowledge and Information Systems,2015,42(3): 525-544.
    [22]NIE F P, HUANG H, DING C. Low-rank matrix recovery via efficient Schattenp-norm minimization[C]//Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence. 2012: 655-661.
    [23]CAO W F, SUN J, XU Z B. Fast image deconvolution using closed-form thresholding formulas of Lq(q=1/2, 2/3) regularization[J].Journal of Visual Communication and Image Representation,2013, 24(1): 31-41.
    [24]ZHANG Y, YE W Z. L2/3 regularization: convergence of iterative thresholding algorithm[J].Journal of Visual Communication and Image Representation,2015,33: 350-357.
    [25]WANG Z, GAO C, LUO X H, et al. Accelerated inexact matrix completion algorithm via closed-formq-thresholding (q=1/2,2/3) operator[J].International Journal of Machine Learning and Cybernetics,2020,11: 2327-2339.
    [26]LAI M, LIU L. A new estimate of restricted isometry constants for sparse solutions[J].Applied and Computational Harmonic Analysis,2011,30(3): 402-406.
    [27]CHARTRAND R, STANEVA V. Restricted isometry properties and nonconvex compressive sensing[J].Inverse Problems,2010, 24(3): 657-682.
    [28]HE S, WANG Y, WANG J, et al. Block-sparse compressed sensing with partially known signal support via non-convex minimization[J].IET Signal Processing,2016,10(7): 717-723.
    [29]BOYD S, PARIKH N, CHU E, et al. Distributed optimization and statistical learning via the alternating direction method of multipliers[J].Foundations Trends in Machine Learning,2011,3(1): 1-122.
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出版历程
  • 收稿日期:  2021-01-11
  • 修回日期:  2021-04-06
  • 网络出版日期:  2021-09-29

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