Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aigu Liwubuli., 2015, Research on image enhancement methods based on shearlet and NSST transform:MSc. Thesis, **njiang University.
Chang D.K., Yang W.Y., Wang Y.H., et.al., 2018, Random noise suppression of seismic data using non-local Bayes algorithm:Applied Geophysics, 15(1), P91–98.
Dabov K., Foi A., Katkovnik V., et al., 2007. Image denoising by sparse 3-D transform-domain collaborative filtering:IEEE Transaction on Signal Processing, 16(8), 2080–2095.
D. Kingma and J. Ba, 2015, “Adam: A method for stochastic optimization,” in International Conference for Learning Representations.
Fan J.C., Liu M.J., Wang F.Y., et al., 2009, Wavelet packet node domain and spatial domain dip scan high order correlation denoising technology: Oil Geophysical Prospecting, 44(6), 695–699.
Goodfellow I, Pouget-Abadie J, Mirza M, et al., 2014, Generative Adversarial Nets:MIT Press. Huang D.Y., 2018, Research on wavelet neural network denoising based on sampling principle:MSc. Thesis, University of Electronic Science and Technology of China.
Li H., Li G.F., Ma X., et. al., 2021, Multichannel deconvolution with spatial reflection regularization: Applied Geophysics, 18(1), P65–93.
Li G.F., Li G.S., Zhang L.Q., et al., 1998, Random noise attenuation of seismic data using time-space prediction:Oil Geophysical Prospecting, 33 (Supp.1), 122–128.
Li Y., Wang S.Q., Deng C.Z., 2011. Overview on image denoising based on multi-scale geometric analysis:Computer Engineering and Applications, 47(34), 168–173.
Liu D., Jia J.L., Zhao Y.Q., et al, 2021a. Overview of image denoising methods based on deep learning:Computer Engineering and Applications, 57(7), 1–13.
Liu P.J., Zhang H.Z., Zhang K., et.al, 2018, Multi-level Wavelet-CNN for Image Restoration:IEEE.
Liu X.Z., Hu T.Y., Liu T., et. al, 2022, Seismic multiple suppression method by using of data augmentation CODEC Convolutional network:Oil Geophysical Prospecting, 57(4), 757–767.
Liu Y., 2021b, Research on Huber loss function based image denoising algorithm:MSc. Thesis, Guangdong University of Finance and Economics.
Lv Z.Y., 2021, Research on image denoising based on multi-scale geometric decomposition and neural network:PhD Thesis, Dalian University of Technology.
Ma K., 2014, Multi-scale geometric analysis theory and application research of infrared image:MSc. Thesis, University of Electronic Science and Technology of China.
Mallat S., Hwang W.L., 1992, Singularity detection and processing with wavelets:IEEE Trans Inform Theory, 38(2), 617–643.
Tang F., 2014. Research on image denoising methods based on contourlet transform and shearlet transform: MSc. Thesis, **angtan University.
Walden A.T., Contreras Cristan A., 1998, The phase-corrected undecimated discrete wavelet packet transform and its application to interpreting the timing of events:Proceedings of the Royal Society of London, Series A(454) 2243–2266.
Wei H.T., Lu W.K., Zheng X.D., 2011, Serial filter based on F-X domain prediction and total variation:Oil Geophysical Prospecting, 46(5), 700–704.
Wu A.J., 2011, SAR image denoising based on undecimated wavelet packet decomposition:MSc. Thesis, **’an University of Electronic Science and Technology.
Wu G.N., Yu M.M., Wang J.X., et al., 2022, Stationary wavelet transform and deep residual network are used to suppress seismic random noise:Oil Geophysical Prospecting, 2022, 57(1), 43–51.
**ang Q., Lin C.S., Wu Z.G., 2003, Detection of signal in nonstationary and non-Gaussian background noise:Journal of Wuhan University of Technology (Transportation Science & Engineering), 27(3), 354–357.
Zhang D.L., Huang D.N., Yu P., et.al., 2017a, Translation-invariant denoising of full-tensor Gravity-gradiometer data:Applied Geophysics, 14(4), P606–619.
Zhang K., Zuo W.M., Chen Y.J., et al., 2017b, Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising:IEEE Transactions on Image Processing, 26(7), 3142–3155.
Zhang K, Zuo W, Zhang L., 2018, FFDNet: Toward a fast and flexible solution for CNN-based image denoising:IEEE Transactions on Image Processing, 27(9), 4608–4622.
Zhang J., Chen X.H., Jiang W., et al., 2020, Seismic wavelet extraction in depth domain based on subspace constrained Huber norm:Oil Geophysical Prospecting, 55(6), 1231–1236, 1244.
Zhang M., Liu Y., Chen Y.K., 2019, Unsupervised Seismic Random Noise Attenuation Based on Deep Convolutional Neural Network:IEEE Access, 7, 179810–179822.
Zhang Y., Li X.Y., Wang B., et al, 2022, Robust seismic data denoising based on deep learning:Oil Geophysical Prospecting, 57(1), 12–25.
Zhu H., Huang H.N., Li Y.Q., et al, 1990, Random signal analysis:Bei**g Institute of Technology Press, China, 282–286.
Acknowledgment
This work was supported by the Henan Province Seismic Structure Exploration project (YCZC-2020-950), the Special Fund of the Chinese Central Government for Basic Scientific Research Operations in Commonweal Research Institutes (No. IGCEA2008), the Scientific and Technological Key Project of Henan Province(232102320018).
Author information
Authors and Affiliations
Corresponding author
Additional information
Fan Hua, graduated from China University of Geosciences Bei**g with a Master’s degree in structural geology. She is currently an engineer focusing on seismic disaster prevention and digital image processing.
Corresponding author: Zhang Yang, Senior Engineer. mainly researches active tectonics and basin evolutionary dynamics mechanisms. (Email: 949510935@qq.com)
Rights and permissions
About this article
Cite this article
Fan, H., Wang, DB., Zhang, Y. et al. Suppression of seismic random noise by deep learning combined with stationary wavelet packet transform. Appl. Geophys. (2024). https://doi.org/10.1007/s11770-024-1107-6
Received:
Revised:
Published:
DOI: https://doi.org/10.1007/s11770-024-1107-6