基于原子曲线拟合的字典学习的信号去噪方法

系统仿真学报 ›› 2015, Vol. 27 ›› Issue (12): 2935-2941.

基于原子曲线拟合的字典学习的信号去噪方法

高博, 王俊, 张各各

西安电子科技大学雷达信号处理国家重点实验室,西安 710071

收稿日期:2015-06-10 修回日期:2015-07-23 出版日期:2015-12-08 发布日期:2020-07-30
作者简介:高博(1986-),男,陕西,博士生,研究方向为外辐射源雷达信号处理;王俊(1969-),男,贵州,博士,教授,博导,研究方向为双基地雷达信号处理;张各各(1986-),女,河南,博士生,研究方向为外辐射源雷达信号处理。
基金资助:
国家自然科学基金(61372136)

Signal Denoising Method Based on Atom Curve Fitting Improved Dictionary Learning

Gao Bo, Wang Jun, Zhang Gege

National Key Lab of Radar Signal Processing, Xidian Univ. , Xi’an 710071, China

Received:2015-06-10 Revised:2015-07-23 Online:2015-12-08 Published:2020-07-30

摘要/Abstract

摘要： 在信号去噪问题中,利用K-means Singular Value Decomposition(K-SVD)等经典字典学习算法,对信号进行稀疏分解与信号重构,不能有效的消除噪声影响。引入了非线性最小二乘和粒子群优化的方法对经典的字典学习去噪方法进行了改进。利用K-SVD算法进行字典训练;利用非线性最小二乘的方法对字典中的每一个原子进行拟合,得到修正后的字典;利用粒子群优化的方法求解信号的稀疏表示,最终得到重构信号。通过实验证明,该方法去除噪声的效果相较于K-SVD和RLS-DLA(递归最小二乘字典学习算法)有明显提高。

关键词: 字典学习, 去噪, 粒子群优化, 信号重构, 曲线拟合

Abstract: In signal denoising problems, using K-SVD and other classic dictionary learning algorithm can not effectively eliminate the noise impact. The method made some amendments for classical dictionary learning by applying nonlinear least squares curve fitting and particle swarm optimization. K-SVD algorithm was used to train the dictionary. Nonlinear least-squares approach was used to fit every atom in the dictionary. Particle swarm optimization method was used to solve the sparse representation of the signal. The reconstructed signal was obtained. The experimental results show that, the denoising effects of the proposed method apparently has increased compared with K-SVD and RLS-DLA.

Key words: dictionary learning, denoising, particle swarm optimization, signal reconstruction, curve fitting

中图分类号:

TN911

高博, 王俊, 张各各. 基于原子曲线拟合的字典学习的信号去噪方法[J]. 系统仿真学报, 2015, 27(12): 2935-2941.

Gao Bo, Wang Jun, Zhang Gege. Signal Denoising Method Based on Atom Curve Fitting Improved Dictionary Learning[J]. Journal of System Simulation, 2015, 27(12): 2935-2941.

参考文献

[1] D L Donoho.De-noising by soft-thresholding[J]. IEEE Transactions on Information Theory (S0018-9448), 1995, 41(3): 613-627.
[2] A Pizurica, W Philips.Estimating the probability of the presence of a signal of interest in multiresolution single and multiband image denoising[J]. IEEE Transactions on Image Processing (S1057-7149), 2006, 15(3): 654-665.
[3] J Portilla, V Strela, M J Wainwright, et al. Image denoising using scale mixtures of gaussians in the wavelet domain[J]. IEEE Transactions on Image Processing (S1057-7149), 2003, 12(11): 1338-1351.
[4] L Zhang, P Bao, X Wu Multiscale.LMMSE-based image denoising with optimal wavelet selection[J]. IEEE Transactions on Circuits and System for Video Technology (S1051-8215), 2005, 15(4): 469-481.
[5] 徐晓刚, 徐冠雷, 王孝通, 等. 经验模态分解及其应用[J]. 电子学报, 2009, 37(3): 581-585.
(Xu Xiaogang, Xu Guanlei, Wang Xiaotong, et al. Empirical mode decomposition and its application[J]. Acta Electronica Sinica (S0372-2112), 2009, 37(3): 581-585.)
[6] 王文波, 张晓东, 汪祥莉, 基于主成分分析的经验模态分解消噪方法[J]. 电子学报 2013, 41(7): 1425-1430.
(Wang Wenbo, Zhang Xiaodong, Wang Xiangli.Empirical Mode Decomposition De-noising Method Based on Principal Component Analysis[J]. Acta Electronica Sinica (S0372-2112), 2013, 41(7): 1425-1430.)
[7] Ahron M, Elad M., Bruckstein A M.K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation[J]. IEEE Transactions on Image Processing (S1057-7149), 2006, 15(11): 4311-4322.
[8] Elad M, Abaron M.Image denoising via sparse and redundant representations over learned dictionaries[J]. IEEE Transactions on Image Processing (S1057-7149), 2006, 15(12): 3736-3745.
[9] Rubinstein R, Peleg T, Elad M.Analysis K-SVD: A Dictionary-Learning Algorithm for the Analysis Sparse Model[J]. Signal Processing (S0165-1684), 2013, 2013(61): 661-677.
[10] Djurović I, Djukanović S, Simeunović M, et al. An efficient joint estimation of wideband polynomial-phase signal parameters and direction-of-arrival in sensor array[J]. EURASIP Journal on Advances in Signal Processing (S1687-6180), 2012, 2012(43): 1-19.
[11] Ou Guojian, Yang Shizhong, Jiang Qingping, et al. A Dictionary Learning Algorithm for Denoising Cubic Phase Signal[J]. Journal of Electronics & Information Technology (S1009-5896), 2014, 36(2): 255-259.
[12] Zhuolin Jiang, Zhe Lin, Davis L S.Label Consistent K-SVD: Learning a Discriminative Dictionary for Recognition[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence (S0162-8828), 2013, 2013(35): 2651-2664.
[13] Vivek Soni, Ashish Kumar Bhandari, Anil Kumar, et al. Improved sub-band adaptive thresholding function for denoising of satellite image based on evolutionary algorithms[J]. IET Signal Processing (S1751-9675), 2013, 7(8): 720-730.
[14] G G Bhutada, R S Anand, S C Saxena.PSO-based learning of sub-band adaptive thresholding function for image denoising[J]. Signal Image and Video Processing (S1863-1703), 2013, 6(1): 1-7.
[15] Wang Zonghu, Liu Zhijing, Chen Donghui.Improved PSO-based fast clustering algorithm[J]. Journal of Xidian University (S1001-2400), 2012, 39(5):61-78.