数学形态学和K-SVD字典学习在大地电磁数据去噪中的应用

De-noising magnetotelluric data based on mathematical morphology and K-SVD dictionary learning

为解决大地电磁(Magnetotelluric,MT)常规的时间域去噪方法对于1 Hz附近噪声压制的局限性问题,提出了一种基于数学形态滤波(Mathematical morphological filtering,MMF)和K-SVD(K-Singular value decomposition)字典学习的新型去噪方法,用于压制MT信号中低频数据1Hz附近的强人文噪声。首先,利用MMF分离出低频信号,对该低频信号进行保护以防止信号丢失;然后,使用K-SVD字典学习对剩余的含噪信号进行处理,通过从观测数据中自主学习获取噪声的特征结构,提取噪声轮廓,达到去除噪声的目的。利用一个合成数据集验证算法后,对两个实测数据进行处理,结果表明:该方法可以在几乎不损失有效信号的前提下,消除各种强人文噪声,信噪比大幅提升,数据质量得到很大改善,且去噪效果优于小波变换等传统方法。

In order to solve the problem that the conventional magnetotelluric(MT)time-domain denoising methods have the limitation of damageing low-frequency signal,a new method based on mathematical morphological filtering(MMF)and K-singular value decomposition(K-SVD)dictionary learning was proposed to suppress strong cultural noise near 1Hz of MT data.First,MMF was used to separate the low-frequency signal and protect it entirely.Second,K-SVD dictionary learning was used to process residual noisy signals.The field data was used to extract noise contours from auto-learning cultural noise features,which could achieve the purpose of removing noise.The method was verified by testing a synthetic data set and then was used to process two measured data sets.The results show that the proposed method can eliminate all kinds of strong cultural noises without losing useful signals and improve the signal-to-noise ratio and data quality.Moreover,the denoising effect of the proposed method is better than the traditional methods such as wavelet transform.