搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

混沌信号的压缩感知去噪

李广明 吕善翔

引用本文:
Citation:

混沌信号的压缩感知去噪

李广明, 吕善翔

Chaotic signal denoising in a compressed sensing perspective

Li Guang-Ming, Lü Shan-Xiang
PDF
导出引用
  • 对非线性时间序列进行噪声抑制是从中提取有效信息的前提. 混沌信号的去噪算法不仅要使滤波后的信号具有较高的信噪比, 也要具有较好的不确定性. 从压缩感知的角度出发,提出了一种新的噪声抑制方法. 该方法包括估计噪声方差, 以及依据动态的稀疏度将观测值往确定的过完备字典上投影. 仿真实验表明, 该方法比常用的小波阈值法和局部曲线拟合法具有更高的输出信噪比, 而原始信号的混沌特性也能得到较大程度的恢复.
    Nonlinear time series denoising is the premise for extracting useful information from an observable, for the applications in analyzing natural chaotic signals or achieving chaotic signal synchronizations. A good chaotic signal denoising algorithm processes not only a high signal-to-noise ratio (SNR), but also a good unpredictability of a signal. Starting from the compressed sensing perspective, in this work we provide a novel filtering algorithm for chaotic flows. The first step is to estimate the strength of the noise variance, which is not explicitly provided by any blind algorithm. Then the second step is to construct a deterministic projection matrix, whose columns are polynomials of different orders, which are sampled from the Maclaurin series. Since the noise variance is provided from the first step, then a sparsity level with regard to this signal can be fully constructed, and this sparsity value in conjunction with the orthogonal matching pursuit algorithm is used to recover the original signal. Our method can be regarded as an extension to the local curve fitting algorithm, where the extension lies in allowing the algorithm to choose a wider range of polynomial orders, not just those of low orders. In the analysis of our algorithm, the correlation coefficient of the proposed projection matrix is given, and the reason for shrinking the sparsity when the noise variance increases is also presented, which emphasizes that there is a larger probability of error column selection with larger noise variance. In the simulation, we compare the denoising performance of our algorithm with those of the wavelet shrinking algorithm and the local curve fitting algorithm. In terms of SNR improvement for the Lorenz signal, the proposed algorithm outperforms the local curve fitting method in an input SNR range from 0 dB to 20 dB. And this superiority also exists if the input SNR is larger than 9 dB when compared with the wavelet methods. A similar performance also exists concerning the Rössler chaotic system. The last simulation shows that the chaotic properties of the originals are largely recovered by using our algorithm, where the quantity for "chaotic degree" is described by using the proliferation exponent.
    • 基金项目: 国家自然科学基金(批准号: 61170216, 61372082)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61170216, 61372082).
    [1]

    Wang S Y, Feng J C 2012 Acta Phys. Sin. 61 170508 (in Chinese) [王世元, 冯久超 2012 物理学报 61 170508]

    [2]

    Feng J C 2012 Chaotic Signals and Information Processing (Beijing: Tsinghua Univ. Press) pp32-35 (in Chinese) [冯久超 2012 混沌信号与信息处理 (清华大学出版社)第32–35页]

    [3]

    Lü S X, Feng J C 2013 Acta Phys. Sin. 62 230503 (in Chinese) [吕善翔, 冯久超 2013 物理学报 62 230503]

    [4]

    Feng J C 2005 Chin. Phys. Lett. 22 1851

    [5]

    Feng J C, Tse C K 2001 Phys. Rev. E 63 026202

    [6]

    Constantine W L B, Reinhall P G 2001 Int. J. Bifurcat. Chaos 11 483

    [7]

    Han M, Liu Y H, Xi J H, Guo W 2007 IEEE Signal Process. Lett. 14 62

    [8]

    Gao J B, Sultan H, Hu J, Tung W W 2010 IEEE Signal Process. Lett. 17 237

    [9]

    Tung W W, Gao J B, Hu J, Yang L 2011 Phys. Rev. E 83 046210

    [10]

    Wang W B, Zhang X D, Wang X L 2013 Acta Phys. Sin. 62 050201 (in Chinese) [王文波, 张晓东, 汪祥莉 2013 物理学报 62 050201]

    [11]

    Candes E, Romberg J, Tao T 2006 Commun. Pure Appl. Math. 59 1207

    [12]

    Lustig M, Donoho D, Pauly J 2007 Magn. Reson. Med. 58 1182

    [13]

    Lustig M, Donoho D, Santos J, Pauly J 2008 IEEE Signal Process. Mag. 25 72

    [14]

    Candes E, Wakin M 2008 IEEE Signal Process. Mag. 25 21

    [15]

    Candes E 2008 C. R. Math. 346 589

    [16]

    Chen S, Donoho D, Saunders M 1998 SIAM J. Sci. Comput. 20 33

    [17]

    Donoho D, Huo X 2001 IEEE Trans. Inf. Theory 47 2845

    [18]

    Figueiredo M, Nowak R, Wright S 2007 IEEE J. Sel. Topics Signal Process. 1 586

    [19]

    Cai T T, Wang L 2011 IEEE Trans. Inf. Theory 57 4680

    [20]

    Donoho D, Drori I, Starck J L 2012 IEEE Trans. Inf. Theory 58 1094

    [21]

    Needell D, Vershynin R 2009 Found. Comput. Math. 9 317

    [22]

    Lü S X, Wang Z S, Hu Z H, Feng J C 2014 Chin. Phys. B 23 010506

    [23]

    Holger K, Thomas S 2004 Nonlinear Time Series Ana- lysis (Cambridge: Cambridge University Press) pp65-74

  • [1]

    Wang S Y, Feng J C 2012 Acta Phys. Sin. 61 170508 (in Chinese) [王世元, 冯久超 2012 物理学报 61 170508]

    [2]

    Feng J C 2012 Chaotic Signals and Information Processing (Beijing: Tsinghua Univ. Press) pp32-35 (in Chinese) [冯久超 2012 混沌信号与信息处理 (清华大学出版社)第32–35页]

    [3]

    Lü S X, Feng J C 2013 Acta Phys. Sin. 62 230503 (in Chinese) [吕善翔, 冯久超 2013 物理学报 62 230503]

    [4]

    Feng J C 2005 Chin. Phys. Lett. 22 1851

    [5]

    Feng J C, Tse C K 2001 Phys. Rev. E 63 026202

    [6]

    Constantine W L B, Reinhall P G 2001 Int. J. Bifurcat. Chaos 11 483

    [7]

    Han M, Liu Y H, Xi J H, Guo W 2007 IEEE Signal Process. Lett. 14 62

    [8]

    Gao J B, Sultan H, Hu J, Tung W W 2010 IEEE Signal Process. Lett. 17 237

    [9]

    Tung W W, Gao J B, Hu J, Yang L 2011 Phys. Rev. E 83 046210

    [10]

    Wang W B, Zhang X D, Wang X L 2013 Acta Phys. Sin. 62 050201 (in Chinese) [王文波, 张晓东, 汪祥莉 2013 物理学报 62 050201]

    [11]

    Candes E, Romberg J, Tao T 2006 Commun. Pure Appl. Math. 59 1207

    [12]

    Lustig M, Donoho D, Pauly J 2007 Magn. Reson. Med. 58 1182

    [13]

    Lustig M, Donoho D, Santos J, Pauly J 2008 IEEE Signal Process. Mag. 25 72

    [14]

    Candes E, Wakin M 2008 IEEE Signal Process. Mag. 25 21

    [15]

    Candes E 2008 C. R. Math. 346 589

    [16]

    Chen S, Donoho D, Saunders M 1998 SIAM J. Sci. Comput. 20 33

    [17]

    Donoho D, Huo X 2001 IEEE Trans. Inf. Theory 47 2845

    [18]

    Figueiredo M, Nowak R, Wright S 2007 IEEE J. Sel. Topics Signal Process. 1 586

    [19]

    Cai T T, Wang L 2011 IEEE Trans. Inf. Theory 57 4680

    [20]

    Donoho D, Drori I, Starck J L 2012 IEEE Trans. Inf. Theory 58 1094

    [21]

    Needell D, Vershynin R 2009 Found. Comput. Math. 9 317

    [22]

    Lü S X, Wang Z S, Hu Z H, Feng J C 2014 Chin. Phys. B 23 010506

    [23]

    Holger K, Thomas S 2004 Nonlinear Time Series Ana- lysis (Cambridge: Cambridge University Press) pp65-74

  • [1] 干红平, 张涛, 花燚, 舒君, 何立军. 基于双极性混沌序列的托普利兹块状感知矩阵. 物理学报, 2021, 70(3): 038402. doi: 10.7498/aps.70.20201475
    [2] 汪书潮, 苏秀琴, 朱文华, 陈松懋, 张振扬, 徐伟豪, 王定杰. 基于弹性变分模态提取的时间相关单光子计数信号去噪. 物理学报, 2021, 70(17): 174304. doi: 10.7498/aps.70.20210149
    [3] 陈炜, 郭媛, 敬世伟. 基于深度学习压缩感知与复合混沌系统的通用图像加密算法. 物理学报, 2020, 69(24): 240502. doi: 10.7498/aps.69.20201019
    [4] 石航, 王丽丹. 一种基于压缩感知和多维混沌系统的多过程图像加密方案. 物理学报, 2019, 68(20): 200501. doi: 10.7498/aps.68.20190553
    [5] 王梦蛟, 周泽权, 李志军, 曾以成. 混沌信号自适应协同滤波去噪. 物理学报, 2018, 67(6): 060501. doi: 10.7498/aps.67.20172470
    [6] 刘柏年, 皇群博, 张卫民, 任开军, 曹小群, 赵军. 集合背景误差方差中小波阈值去噪方法研究及试验. 物理学报, 2017, 66(2): 020505. doi: 10.7498/aps.66.020505
    [7] 李广明, 胡志辉. 基于人工蜂群算法的混沌信号盲提取. 物理学报, 2016, 65(23): 230501. doi: 10.7498/aps.65.230501
    [8] 陈越, 吕善翔, 王梦蛟, 冯久超. 一种基于人工蜂群算法的混沌信号盲分离方法. 物理学报, 2015, 64(9): 090501. doi: 10.7498/aps.64.090501
    [9] 郭静波, 李佳文. 二进制信号的混沌压缩测量与重构. 物理学报, 2015, 64(19): 198401. doi: 10.7498/aps.64.198401
    [10] 王梦蛟, 吴中堂, 冯久超. 一种参数优化的混沌信号自适应去噪算法. 物理学报, 2015, 64(4): 040503. doi: 10.7498/aps.64.040503
    [11] 黄锦旺, 李广明, 冯久超, 晋建秀. 一种无线传感器网络中的混沌信号重构算法. 物理学报, 2014, 63(14): 140502. doi: 10.7498/aps.63.140502
    [12] 黄锦旺, 冯久超, 吕善翔. 混沌信号在无线传感器网络中的盲分离. 物理学报, 2014, 63(5): 050502. doi: 10.7498/aps.63.050502
    [13] 程生毅, 陈善球, 董理治, 刘文劲, 王帅, 杨平, 敖明武, 许冰. 交连值对斜率响应矩阵和迭代矩阵稀疏度的影响. 物理学报, 2014, 63(7): 074206. doi: 10.7498/aps.63.074206
    [14] 郭静波, 汪韧. 基于混沌序列和RIPless理论的循环压缩测量矩阵的构造. 物理学报, 2014, 63(19): 198402. doi: 10.7498/aps.63.198402
    [15] 陈晓, 汪陈龙. 基于赛利斯模型和分数阶微分的兰姆波信号消噪. 物理学报, 2014, 63(18): 184301. doi: 10.7498/aps.63.184301
    [16] 王文波, 张晓东, 汪祥莉. 基于独立成分分析和经验模态分解的混沌信号降噪. 物理学报, 2013, 62(5): 050201. doi: 10.7498/aps.62.050201
    [17] 马原, 吕群波, 刘扬阳, 钱路路, 裴琳琳. 基于主成分变换的图像稀疏度估计方法. 物理学报, 2013, 62(20): 204202. doi: 10.7498/aps.62.204202
    [18] 王世元, 冯久超. 一种新的参数估计方法及其在混沌信号盲分离中的应用. 物理学报, 2012, 61(17): 170508. doi: 10.7498/aps.61.170508
    [19] 谢映海, 杨维, 张玉. 离散空间上的最小能量框架及其在矩形脉冲信号去噪中的应用研究. 物理学报, 2010, 59(11): 8255-8263. doi: 10.7498/aps.59.8255
    [20] 游荣义, 陈 忠, 徐慎初, 吴伯僖. 基于小波变换的混沌信号相空间重构研究. 物理学报, 2004, 53(9): 2882-2888. doi: 10.7498/aps.53.2882
计量
  • 文章访问数:  4860
  • PDF下载量:  504
  • 被引次数: 0
出版历程
  • 收稿日期:  2015-03-25
  • 修回日期:  2015-05-23
  • 刊出日期:  2015-08-05

混沌信号的压缩感知去噪

  • 1. 东莞理工学院计算机学院, 东莞 523808;
  • 2. 华南理工大学电子与信息学院, 广州 510641
    基金项目: 国家自然科学基金(批准号: 61170216, 61372082)资助的课题.

摘要: 对非线性时间序列进行噪声抑制是从中提取有效信息的前提. 混沌信号的去噪算法不仅要使滤波后的信号具有较高的信噪比, 也要具有较好的不确定性. 从压缩感知的角度出发,提出了一种新的噪声抑制方法. 该方法包括估计噪声方差, 以及依据动态的稀疏度将观测值往确定的过完备字典上投影. 仿真实验表明, 该方法比常用的小波阈值法和局部曲线拟合法具有更高的输出信噪比, 而原始信号的混沌特性也能得到较大程度的恢复.

English Abstract

参考文献 (23)

目录

    /

    返回文章
    返回