基于压缩感知的地震勘探随机噪声消减算法研究

The research of the seismic prospecting random noise attenuation algorithm based on compressive sensing

为有效提高地震勘探记录的信噪比,文中将基于压缩感知理论的梯度投影稀疏重建(GPSR)算法引入到地震勘探随机噪声压制领域。该方法首先将含噪信号通过压缩感知理论进行稀疏表示,在此基础上通过GPSR算法对信号进行重构。重构过程可以视为病态矩阵的求解过程,由于正则项的约束,在重构过程中可以有效地压制含噪信号中的噪声。实验结果表明,该算法在有效地消减随机噪声的同时,也可以较好的保持有效信号的幅度。将该算法的处理结果同传统维纳滤波处理结果进行比较分析,表明该算法的处理效果要好于传统的维纳滤波算法。

In order to increase the signal to noise ratio, we attempt to apply the Gradient Projection for Square Reconstruction（GPSR） algorithm, which is based on compressive sensing theory, to suppress the random noise in seismic prospecting data.First, we use compressive sensing to get the sparse representation of the noised signal. On this basis, GPSR algorithm is used to reconstruct the signal. The reconstruction procedure can be viewed as solving an ill-conditioned matrix. Due to the regularization item, the noise can be suppressed effectively during the reconstruction procedure. The results show that this algorithm can attenuate the random noise effectively and protect amplitude of the effective events properly. We also make a comparison between the performances of the GPSR algorithm and the Wiener filtering. It shows that the GPSR algorithm works better than Wiener filtering in terms of denoising results.