Suppression of seismic random noise by deep learning combined with stationary wavelet packet transform

Many traditional denoising methods, such as Gaussian filtering, tend to blur and lose details or edge information while reducing noise. The stationary wavelet packet transform is a multi-scale and multi-band analysis tool. Compared with the stationary wavelet transform, it can suppress high-frequency noise while preserving more edge details. Deep learning has significantly progressed in denoising applications. DnCNN, a residual network; FFDNet, an efficient, flexible network; U-NET, a codec network; and GAN, a generative adversative network, have better denoising effects than BM3D, the most popular conventional denoising method. Therefore, SWP_hFFDNet, a random noise attenuation network based on the stationary wavelet packet transform (SWPT) and modified FFDNet, is proposed. This network combines the advantages of SWPT, Huber norm, and FFDNet. In addition, it has three characteristics: First, SWPT is an effective feature-extraction tool that can obtain low- and high-frequency features of different scales and frequency bands. Second, because the noise level map is the input of the network, the noise removal performance of different noise levels can be improved. Third, the Huber norm can reduce the sensitivity of the network to abnormal data and enhance its robustness. The network is trained using the Adam algorithm and the BSD500 dataset, which is augmented, noised, and decomposed by SWPT. Experimental and actual data processing results show that the denoising effect of the proposed method is almost the same as those of BM3D, DnCNN, and FFDNet networks for low noise. However, for high noise, the proposed method is superior to the aforementioned networks.