一种基于压缩感知的随机噪声压制方法

随着高精度地震勘探技术的发展，利用高保真的方法提高地震资料信噪比成为了去噪处理的关键。曲波域阈值法能够有效地压制随机噪声，但易产生伪吉布斯震荡现象，造成信号局部畸变，从而影响处理效果。针对这一问题，提出一种基于压缩感知理论（Compressing Sensing，简称CS）的地震信号去噪方法，该方法利用随机噪声和有效信号在曲波稀疏域稀疏表征的差异来分离随机噪声。其实现步骤为:将地震数据变换到曲波域；利用压缩感知理论和全变差正则化算法重构曲波系数；曲波逆变换得到压制噪声后的重构地震数据。理论模型和实际资料应用表明，该方法能够很好规避伪吉布斯现象带来的信号失真问题，进一步提高了资料的信噪比。 

A method of random noise suppression based on compressed sensing

With the development of high precision seismic exploration technology, the use of high fidelity methods to improve the SNR of seismic data becomes the key to denoising. Curvelet threshold method can effectively suppress random noise, but at the same time the method is easy to produce pseudo Gibbs shock phenomenon, resulting in local distortion of the signal, thus affecting the processing effect. To solve this problem, a method of seismic signal denoising based on compressing sensing(CS) is presented in this paper. The method uses the difference between sparse representation of random noise and effective signal in curvelet sparse domain to suppress the separation of random noise. Seismic data are transformed into curvelet domain; Curvelet coefficients are reset by using the compression perception theory and the total variation regularization algorithm; Reconstructed seismic data after curvelet inversion are used to suppress noise. The theoretical model and practical data show that the proposed method can avoid the signal distortion caused by the pseudo-Gibbs phenomenon and further improve the signal-to-noise ratio of the data.