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压缩感知理论在矩量法中的应用

王哲 王秉中

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Citation:

压缩感知理论在矩量法中的应用

王哲, 王秉中

Application of compressed sensing theory in the method of moments

Wang Zhe, Wang Bing-Zhong
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  • 矩阵填充与线性方程组求解是矩量法中最耗计算资源的环节. 为提高计算效率,提出了一种基于压缩感知理论的矩量法的改进方法. 通过引入稀疏变换矩阵实现对待求响应的稀疏表示,从而可在压缩感知理论框架下构造欠定方程,并优化求解. 数值仿真实验结果表明:该方法不仅可以减小矩阵填充计算量,还可以有效提高解的求解效率.
    Matrix filling and equation solving are the most computationally-expensive steps in the method of moments (MoM). Based on the compressed sensing (CS) theory, an improved method of MoM is proposed in this paper. Through introducing sparse transform matrix, the unknown response can be expressed sparsely, so we can construct and optimally solving underdetermined equation under the framework of CS. Numerical examples show that the proposed method can reduce the matrix filling cost dramatically, and also can improve the efficiency of equation solving effectively.
    • 基金项目: 国家自然科学基金(批准号:61071031,61331007)和高等学校博士学科点专项科研基金(批准号:20100185110021,20120185130001)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61071031, 61331007) and the Specia- lized Research Fund for the Doctoral Program of Higher Education of China (Grant Nos. 20100185110021, 20120185130001).
    [1]

    Hanington R F 1968 Field Computation by Moment Methods (New York: Maxillan) p6

    [2]

    Nie Z P, Wang H G 2003 Acta Phys. Sin. 52 3035 (in Chinese) [聂在平, 王浩刚 2003 物理学报 52 3035]

    [3]

    Ma J, Guo L X, Wang A Q 2009 Chin. Phys. B 18 3431

    [4]

    Steinberg B Z, Leviatan Y 1993 IEEE Trans. Antennas Propagat. 41 610

    [5]

    Jrgensen E, Volakis J L, Meincke P, Breinbjerg O 2004 IEEE Trans. Antennas Propag. 52 2985

    [6]

    Gao Q, Yi S H, Jiang Z F, Zhao Y X, Xie W K 2012 Chin. Phys. B 21 064701

    [7]

    Wang L Y, Li L, Yan B 2010 Chin. Phys. B 19 088106

    [8]

    Donoho D L 2006 IEEE Trans. Inform. Theory 52 1289

    [9]

    Baraniuk R G 2007 IEEE Sig. Proc. Mag. 24 118

    [10]

    Tao T 2005 Math. Res. Lett. 12 121

    [11]

    Candès E J 2008 Comptes Rendus Mathematique 346 589

    [12]

    Pati Y C, Rezaiifar R, Krishnaprasad P S 1993 Proc. 27th Annu. Asilomar Conf. Signals, Systems, and Computers Pacific Grove, U.S.A., Nov. 1-3, 1993 p40

    [13]

    Bai X, Li Y Q, Zhao S M 2013 Acta Phys. Sin. 62 044209 (in Chinese) [白旭, 李永强, 赵生妹 2013 物理学报 62 044209]

    [14]

    Kutyniok G 2012 CoRR abs/1203 3815

    [15]

    Chen S S, Donoho D L, Saunders M A 2001 SIAM Rev. 43 129

    [16]

    Chen M S, Liu F L, Du H M, Wu X L 2011 IEEE Anten. Wireless Propag. Lett. 10 1243

  • [1]

    Hanington R F 1968 Field Computation by Moment Methods (New York: Maxillan) p6

    [2]

    Nie Z P, Wang H G 2003 Acta Phys. Sin. 52 3035 (in Chinese) [聂在平, 王浩刚 2003 物理学报 52 3035]

    [3]

    Ma J, Guo L X, Wang A Q 2009 Chin. Phys. B 18 3431

    [4]

    Steinberg B Z, Leviatan Y 1993 IEEE Trans. Antennas Propagat. 41 610

    [5]

    Jrgensen E, Volakis J L, Meincke P, Breinbjerg O 2004 IEEE Trans. Antennas Propag. 52 2985

    [6]

    Gao Q, Yi S H, Jiang Z F, Zhao Y X, Xie W K 2012 Chin. Phys. B 21 064701

    [7]

    Wang L Y, Li L, Yan B 2010 Chin. Phys. B 19 088106

    [8]

    Donoho D L 2006 IEEE Trans. Inform. Theory 52 1289

    [9]

    Baraniuk R G 2007 IEEE Sig. Proc. Mag. 24 118

    [10]

    Tao T 2005 Math. Res. Lett. 12 121

    [11]

    Candès E J 2008 Comptes Rendus Mathematique 346 589

    [12]

    Pati Y C, Rezaiifar R, Krishnaprasad P S 1993 Proc. 27th Annu. Asilomar Conf. Signals, Systems, and Computers Pacific Grove, U.S.A., Nov. 1-3, 1993 p40

    [13]

    Bai X, Li Y Q, Zhao S M 2013 Acta Phys. Sin. 62 044209 (in Chinese) [白旭, 李永强, 赵生妹 2013 物理学报 62 044209]

    [14]

    Kutyniok G 2012 CoRR abs/1203 3815

    [15]

    Chen S S, Donoho D L, Saunders M A 2001 SIAM Rev. 43 129

    [16]

    Chen M S, Liu F L, Du H M, Wu X L 2011 IEEE Anten. Wireless Propag. Lett. 10 1243

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  • PDF下载量:  832
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-12-13
  • 修回日期:  2014-03-01
  • 刊出日期:  2014-06-05

压缩感知理论在矩量法中的应用

  • 1. 电子科技大学应用物理研究所, 成都 610054
    基金项目: 

    国家自然科学基金(批准号:61071031,61331007)和高等学校博士学科点专项科研基金(批准号:20100185110021,20120185130001)资助的课题.

摘要: 矩阵填充与线性方程组求解是矩量法中最耗计算资源的环节. 为提高计算效率,提出了一种基于压缩感知理论的矩量法的改进方法. 通过引入稀疏变换矩阵实现对待求响应的稀疏表示,从而可在压缩感知理论框架下构造欠定方程,并优化求解. 数值仿真实验结果表明:该方法不仅可以减小矩阵填充计算量,还可以有效提高解的求解效率.

English Abstract

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