ZHOU Jun, HUANG Wei. Improved Conditions for Block-Sparse Signal Recovery via the Non-Convex Optimization Model[J]. Applied Mathematics and Mechanics, 2019, 40(2): 167-180. doi: 10.21656/1000-0887.390154
Citation: ZHOU Jun, HUANG Wei. Improved Conditions for Block-Sparse Signal Recovery via the Non-Convex Optimization Model[J]. Applied Mathematics and Mechanics, 2019, 40(2): 167-180. doi: 10.21656/1000-0887.390154

Improved Conditions for Block-Sparse Signal Recovery via the Non-Convex Optimization Model

doi: 10.21656/1000-0887.390154
Funds:  The Major Research Plan of the National Natural Science Foundation of China(91538112); The National Science Fund for Young Scholars of China(11201450)
  • Received Date: 2018-05-25
  • Rev Recd Date: 2018-12-04
  • Publish Date: 2019-02-01
  • Compressed sensing (CS) is a newly developed theoretical framework for information acquisition and processing, which shows that sparse signals can be recovered exactly from far less samples than those required by the classical ShannonNyquist theorem. The blocksparse signal recovery algorithm under the compressed sensing framework was mainly studied, and a class of improved exact recovery conditions based on the block restricted isometry property (RIP) were established in the noiseless cases via the mixed l2/lq(0
  • loading
  • [1]
    DONOHO D. Compressed sensing[J]. IEEE Transactions on Information Theory,2006,52(4): 1289-1306.
    [2]
    CANDES E J, ROMBERG J, TAO T. Stable signal recovery from incomplete and inaccurate measurements[J]. Communications Pure and Applied Mathematics,2006,59(8): 1207-1223.
    [3]
    CANDES E J. The restrictedisometry property and its implications for compressed sensing[J]. Comptes Rendus Mathematique,2008,346(9/10): 589-592.
    [4]
    CAI T, WANG L, XU G W. New bounds for restricted isometry constants[J]. IEEE Transactions on Information Theory,2010,56(9): 4388-4394.
    [5]
    CAI T, ZHANG A R. Compressed sensing and affine rank minimization under restricted isometry[J]. IEEE Transactions on Signal Processing,2013,61(13): 3279-3290.
    [6]
    FOUCART S. A note on guaranteed sparse recovery via l1-minimization[J]. Applied and Computational Harmonic Analysis,2010,29(1): 97-103.
    [7]
    DAVIES M, GRIBONVAL R. Restricted isometry constants where lp sparse recovery can fail for 0
    [8]
    LUSTIG M, DONOHO D L, PAULY J M. Rapid MR imaging with compressed sensing and randomly under-sampled 3DFT trajectories[C]// Proceeding of the 〖STBX〗14th Annual Meeting of ISMRM. Seattle, USA, 2006.
    [9]
    DUARTE M, DAVENPORT M, TAKBAR D, et al. Single-pixel imaging via compressive sampling[J]. IEEE Signal Processing Magazine,2008,25(2): 83-91.
    [10]
    BARANIUK R, STEEGHS P. Compressive radar imaging[C]// Proceeding of the IEEE Radar Conference . Washington DC, USA, 2007.
    [11]
    BAJWA W, HAUPT J, SAYEED A, et al. Joint source-channel communication for distributed estimation in sensor networks[J]. IEEE Transactions on Information Theory,2007,53(10): 3629-3653.
    [12]
    ELDER Y, MISHALI M. Robust recovery of signals from a structured union of subspaces[J]. IEEE Transactions on Information Theory,2009,55(11): 5302-5316.
    [13]
    MISHALI M, ELDAR Y. Blind multiband signalreconstruction: compressed sensing for analog signals[J]. IEEE Transactions on Signal Processing,2009,57(3): 993-1009.
    [14]
    DAI W,SHEIKH M A, MILENKOVIC O, et al. Compressed sensing DNA microarrays[J]. EURASIP Journal on Bioinformatics and Systerms Biology,2009,2009(1): 162824.
    [15]
    ENDER J. On compressive sensing applied to radar[J]. Signal Processing,2010,90(5): 1402-1414.
    [16]
    YANG Z, XIE L. Continuous compressed sensing with a single or multiple measurement vectors[C]//2014 IEEE Workshop on Statistical Signal Processing(SSP),2014: 308-311. DOI: 10.1109/SSP.2014.6884632.
    [17]
    LIN J H, LI S. Block sparse recovery via mixed l2/l1 minimization[J]. Acta Mathematica Sinica,2013,29(7): 1401-1412.
    [18]
    CHEN W, LI Y. The high order block RIP condition for signal recovery[J]. Journal of Computational Mathematics,2016,37(1): 61-75.
    [19]
    ZHOU Shenglong, KONG Lingchen, LUO Ziyan, et al. New RIC bounds via lq-minimization with 0
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1276) PDF downloads(585) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return