压缩感知测量矩阵的有限等距常数估计方法

详细信息    查看全文 | 推荐本文 |

英文篇名：A method of restricted isometry constants estimation for compressed sensing measurement matrices 作者：贾彬彬 ; 刘俊莹 英文作者：JIA Bin-bin;LIU Jun-ying;School of Electrical and Information Engineering,Lanzhou University of Technology;Key Laboratory of Gansu Advanced Control for Industrial Process,Lanzhou University of Technology;National Demonstration Center for Experimental Electrical and Control Engineering Education,Lanzhou University of Technology; 关键词：压缩感知 ; 测量矩阵 ; 有限等距性质 ; 有限等距常数 英文关键词：compressed sensing;;measurement matrices;;restricted isometry property;;restricted isometry constants 中文刊名：HDZJ 英文刊名：Information Technology 机构：兰州理工大学电气工程与信息工程学院;甘肃省工业过程先进控制重点实验室;兰州理工大学电气与控制工程国家级实验教学示范中心; 出版日期：2018-07-24 出版单位：信息技术 年：2018 期：v.42;No.320 基金：甘肃省自然科学基金(1610RJYA007,1610RJYA026);; 甘肃省工业过程先进控制重点实验室开放课题(XJK201517) 语种：中文; 页：HDZJ201807021 页数：4 CN：07 ISSN：23-1557/TN 分类号：94-97

摘要

有限等距常数是评价压缩感知测量矩阵的重要参数之一,例如压缩感知精确重构须保证有限等距常数满足一定的条件,因此求出有限等距常数具有重要意义。然而,有限等距数的求解是一个NP难的问题。提出了广义有限等距常数,可以作为有限等距常数的一个下限估计值,并给出了一种广义有限等距常数的估计方法。实验结果表明估计结果稳定,可用于进一步研究有限等距常数在压缩感知中的作用。
        Restricted isometry constants(RIC) is one of the most important parameters for compressed sensing(CS) measurement matrices evaluation. For example,RIC should meet some conditions to ensure exact reconstruction of CS. Therefore,it is significant to solve out RIC. However,it is a NP-hard problem to solve out RIC. Generalized RIC(GRIC) is proposed,which can be regarded as a lower limit of RIC. Then,a method of GRIC estimation is given out. The GRIC estimation is stable shown by the result of experiments,and it can be used in advanced studies of RIC's impact on CS.

引文

[1]Candes E J,Tao T.Decoding by linear programming[J].IEEE Transactions on Information Theory,2005,51(12):4203-4215.
    [2]Candès E J.The restricted isometry property and its implications for compressed sensing[J].Comptes Rendus Mathematique,2008,346(9):589-592.
    [3]Wang J,Shim B.On the recovery limit of sparse signals using orthogonal matching pursuit[J].IEEE Transactions on Signal Processing,2012,60(9):4973-4976.
    [4]Cai T T,Wang L,Xu G.New bounds for restricted isometry constants[J].IEEE Transactions on Information Theory,2010,56(9):4388-4394.
    [5]Bandeira A S,Dobriban E,Mixon D G,et al.Certifying the Restricted Isometry Property is Hard[J].IEEE Transactions on Information Theory,2013,59(6):3448-3450.
    [6]Tillmann A M,Pfetsch M E.The Computational Complexity of the Restricted Isometry Property,the Nullspace Property,and Related Concepts in Compressed Sensing[J].IEEE Transactions on Information Theory,2014,60(2):1248-1259.
    [7]Baraniuk R,Davenport M,De Vore R,et al.A simple proof of the restricted isometry property for random matrices[J].Constructive Approximation,2008,28(3):253-263.
    [8]张波,刘郁林,王开.稀疏随机矩阵有限等距性质分析[J].电子与信息学报,2014,36(1):169-174.
    [9]党骙,马林华,田雨,等.m序列压缩感知测量矩阵构造[J].西安电子科技大学学报,2015,42(2):186-192.
    [10]朱志臻,周崇彬,刘发林,等.用于压缩感知的二值化测量矩阵[J].微波学报,2014,30(2):79-83,96.
    [11]王学伟,崔广伟,王琳,等.基于平衡Gold序列的压缩感知测量矩阵的构造[J].仪器仪表学报,2014,35(1):97-102.
    [12]陶春贵,魏爽.空间谱估计中的压缩感知测量矩阵分析[J].信息技术,2017(8):5-10.
    [13]李珅,马彩文,李艳,等.压缩感知重构算法综述[J].红外与激光工程,2013,42(S1):225-232.
    [14]Donoho D L,Elad M.Optimally sparse representation in general(nonorthogonal)dictionaries via1 minimization[J].Proceedings of the National Academy of Sciences,2003,100(5):2197-2202.
    [15]史荣昌,魏丰.矩阵分析[M].3版.北京:北京理工大学出版社,2010:144-147.
    [16]吴赟.压缩感知测量矩阵的研究[D].西安:西安电子科技大学,2012.