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受污染混沌信号的协同滤波降噪

陈越 刘雄英 吴中堂 范艺 任子良 冯久超

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受污染混沌信号的协同滤波降噪

陈越, 刘雄英, 吴中堂, 范艺, 任子良, 冯久超

Denoising of contaminated chaotic signals based on collaborative filtering

Chen Yue, Liu Xiong-Ying, Wu Zhong-Tang, Fan Yi, Ren Zi-Liang, Feng Jiu-Chao
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  • 根据混沌吸引子的自相似分形特性,提出了一种利用协同滤波重构受污染混沌信号的降噪算法.所设计的降噪算法通过对相似片段的分组将一维混沌信号的降噪转化为一个二维联合滤波问题;然后,在二维变换域用阈值法衰减噪声;最后,通过反变换获得原始信号的估计.由于分组中的相似片段具有良好的相关性,与直接在一维变换域做阈值降噪相比,分组的二维变换能获得原信号更稀疏的表示,更好地抑制噪声.仿真结果表明,该算法对原始混沌信号的重构精度和信噪比的提升都优于小波阈值、局部曲线拟合等现有的混沌信号降噪方法,对相图的还原质量也更好.
    Reconstructing chaotic signals from noised data plays a critical role in many areas of science and engineering. However, the inherent features, such as aperiodic property, wide band spectrum, and extreme sensitivity to initial values, present a big challenge of reducing the noises in the contaminated chaotic signals. To address the above issues, a novel noise reduction algorithm based on the collaborative filtering is investigated in this paper. By exploiting the fractal self-similarity nature of chaotic attractors, the contaminated chaotic signals are reconstructed subsequently in three steps, i.e., grouping, collaborative filtering, and signal reconstruction. Firstly, the fragments of the noised signal are collected and sorted into different groups by mutual similarity. Secondly, each group is tackled with a hard threshold in the two-dimensional (2D) transforming domain to attenuate the noise. Lastly, an inverse transformation is adopted to estimate the noise-free fragments. As the fragments within a group are closely correlated due to their mutual similarity, the 2D transform of the group should be sparser than the one-dimensional transform of the original signal in the first step, leading to much more effective noise attenuation. The fragments collected in the grouping step may overlap each other, meaning that a signal point could be included in more than one fragment and have different collaborative filtering results. Therefore, the noise-free signal is reconstructed by averaging these collaborative filtering results point by point. The parameters of the proposed algorithm are discussed and a set of recommended parameters is given. In the simulation, the chaotic signal is generated by the Lorenz system and contaminated by addictive white Gaussian noise. The signal-to-noise ratio and the root mean square error are introduced to measure the noise reduction performance. As shown in the simulation results, the proposed algorithm has advantages over the existing chaotic signal denoising methods, such as local curve fitting, wavelet thresholding, and empirical mode decomposition iterative interval thresholding methods, in the reconstruction accuracy, improvement of the signal-to-noise ratio, and recovering quality of the phase portraits.
      通信作者: 刘雄英, liuxy@scut.edu.cn
    • 基金项目: 国家自然科学基金(批准号:61372008)和广东省科技计划项目(批准号:2015B010101006,2014A010103014)资助的课题.
      Corresponding author: Liu Xiong-Ying, liuxy@scut.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61372008) and the Science and Technology Planning Project of Guangdong Province, China (Grant Nos. 2015B010101006, 2014A010103014).
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    Dabov K, Foi A, Katkovnik V, Egiazarian K 2007 IEEE Trans. Image Proc. 16 2080

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    Yu S M 2011 Chaotic Systems and Chaotic Circuits (Xi'an: Xidian University Press) pp10-12 (in Chinese) [禹思敏 2011 混沌系统与混沌电路 (西安: 西安电子科技大学出版社) 第1012页]

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  • [1]

    Feng J C 2012 Chaotic Signals and Information Processing (Beijing: Tsinghua University Press) pp32-35 (in Chinese) [冯久超 2012 混沌信号与信息处理 (北京: 清华大学出版社) 第3235页]

    [2]

    Badii R, Broggi G, Derighetti B, Ravani M, Ciliberto S, Politi A, Rubio M A 1988 Phys. Rev. Lett. 60 979

    [3]

    Liu X Y, Qiu S S, Lau C M 2005 J. Syst. Eng. Electron. 16 253

    [4]

    Cawley R, Hsu G H 1992 Phys. Rev. A 46 3057

    [5]

    Leontitsis A, Bountis T, Pange J 2004 Chaos 14 106

    [6]

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

    [7]

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

    [8]

    Kopsinis Y, McLaughlin S 2009 IEEE Trans. Signal Proc. 57 1351

    [9]

    Wang X F, Qu J L, Gao F, Zhou Y P, Zhang Y X 2014 Acta Phys. Sin. 63 170203 (in Chinese) [王小飞, 曲建岭, 高峰, 周玉平, 张翔宇 2014 物理学报 63 170203]

    [10]

    Wei X L, Lin R L, Liu S Y, Zhang C H 2016 Shock Vib. 2016 1

    [11]

    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]

    [12]

    Li G M, L S X 2015 Acta Phys. Sin. 64 160502 (in Chinese) [李广明, 吕善翔 2015 物理学报 64 160502]

    [13]

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

    [14]

    Wang M J, Wu Z T, Feng J C 2015 Acta Phys. Sin. 64 040503 (in Chinese) [王梦蛟, 吴中堂, 冯久超 2015 物理学报 64 040503]

    [15]

    Hu J F, Zhang Y X, Yang M, Li H Y, Xia W, Li J 2016 Nonlinear Dynam. 84 1469

    [16]

    Donoho D L, Johnstone I M 1994 Biometrika 81 425

    [17]

    Dabov K, Foi A, Katkovnik V, Egiazarian K 2007 IEEE Trans. Image Proc. 16 2080

    [18]

    Lebrun M 2012 Image Proc. On Line 2 175

    [19]

    Yu S M 2011 Chaotic Systems and Chaotic Circuits (Xi'an: Xidian University Press) pp10-12 (in Chinese) [禹思敏 2011 混沌系统与混沌电路 (西安: 西安电子科技大学出版社) 第1012页]

    [20]

    He T, Zhou Z O 2007 Acta Phys. Sin. 56 693 (in Chinese) [贺涛, 周正欧 2007 物理学报 56 693]

    [21]

    Tang Y F, Liu S L, Lei N, Jiang R H, Liu Y H 2012 Acta Phys. Sin. 61 170504 (in Chinese) [唐友福, 刘树林, 雷娜, 姜锐红, 刘颖慧 2012 物理学报 61 170504]

    [22]

    Coifman R R, Donoho D L 1995 Lect. Notes Stat. 103 125

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出版历程
  • 收稿日期:  2017-05-19
  • 修回日期:  2017-06-18
  • 刊出日期:  2017-11-05

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