CEEMD与KSVD字典训练相结合的去噪方法

本文提出一种完备总体经验模态分解（CEEMD）方法与K奇异值分解（KSVD）学习字典算法相结合的地震信号去噪方法。含噪信号通过CEEMD分解得到一系列不同尺度的固有模态函数（IMF）；按频率由高到低依次排列IMF各分量，并做自相关分析，去除噪声主导的IMF分量；将累加的过渡IMF分量叠加重构并做CEEMD二次分解，通过自相关分析再次去除噪声主导的IMF分量；分别叠加二次CEEMD分解剩余的IMF分量和一次剩余的IMF分量，得到两个新的含噪信号，并利用KSVD过完备字典分别稀疏表示该两个新的含噪信号，即由稀疏系数重构去噪后地震信号，进而重构最终去噪结果。实验结果证明：该算法的去噪效果明显优于F-X去噪、小波阈值去噪和KSVD字典稀疏去噪等传统方法。

Seismic denoising with CEEMD and KSVD dictionary combined training

Combining the complete ensemble empirical mode decomposition (CEEMD) and the K singular value decomposition (KSVD) dictionary algorithm,a seismic denoising is proposed in this paper.A signal with random noise is decomposed by CEEMD into a series of inherent modal functions (IMF) of different scales.The IMF components are arranged from high to low frequency and their autocorrelation eliminates noise-dominant IMF components.Accumulated transitional components are superimposed and reconstructed by CEEMD decomposition again and noise-dominant components are removed again by the autocorrelation.The second remaining IMF components and the first remaining IMF components are superposed to get two new noisy signals which are sparsely represented by KSVD learning dictionary respectively.In the other words,sparse coefficients reconstruct denoised signals.Finally,two sparse denoising signals are reconstructed.Experimental results show that the proposed algorithm can better remove noise than conventional methods such as F-X,wavelet threshold,and KSVD.