Gravity data denoising method based on multilevel wavelet residual network

doi:10.11772/j.issn.1001-9081.2024101545

Journal of Computer Applications ›› 2025, Vol. 45 ›› Issue (10): 3336-3341.DOI: 10.11772/j.issn.1001-9081.2024101545

• Frontier and comprehensive applications • Previous Articles

Gravity data denoising method based on multilevel wavelet residual network

Yali XUE¹(), Zhongmin XU¹^,², Shihao LIU³

^1.College of Automation Engineering，Nanjing University of Aeronautics and Astronautics，Nanjing Jiangsu 211106，China
^2.Huiqin （Changzhou） New Energy Technology Company Limited，Changzhou Jiangsu 213164，China
^3.Beijing Institute of Electronic System Engineering，Beijing 100854，China

Received:2024-10-30 Revised:2024-12-25 Accepted:2024-12-30 Online:2025-01-06 Published:2025-10-10
Contact: Yali XUE
About author:XUE Yali， born in 1974， Ph. D.， associate professor. Her research interests include target detection and recognition， image countermeasures and defense.
XU Zhongmin， born in 1988， assistant engineer. His research interests include engine control.
LIU Shihao， born in 1997， assistant engineer. His research interests include command control and communications.
Supported by:
Shanghai Aerospace Science and Technology Innovation Fund(SAST2022-013)

基于多级小波残差网络的重力数据去噪方法

薛雅丽¹(), 徐忠敏¹^,², 刘世豪³

^1.南京航空航天大学自动化学院，南京 211106
^2.常州慧勤新能源科技有限公司，江苏常州 213164
^3.北京电子工程总体研究所，北京 100854

通讯作者: 薛雅丽
作者简介:薛雅丽（1974—），女，黑龙江集贤人，副教授，博士，主要研究方向：目标检测与识别、图像对抗与防御 Email:xueyali@nuaa.edu.cn
徐忠敏（1988—），男，江苏沛县人，助理工程师，主要研究方向：发动机控制
刘世豪（1997—），男，湖南安化人，助理工程师，主要研究方向：指挥控制与通信。
基金资助:
上海航天科技创新基金资助项目(SAST2022-013)

Abstract

Abstract:

In order to reduce the influence of interference noise on gravity measured data and further improve the accuracy of gravity data processing， a gravity data denoising method based on Multilevel Wavelet Residual Network （MWRNet） was proposed， which combined wavelet transform and neural network to realize removal of noise components in gravity data. Firstly， the gravity data was decomposed by wavelet transform， and then a neural network was utilized for noise extraction， while the Residual Channel Attention （RCA） module was introduced to enhance noise extraction ability of the network. The proposed gravity data denoising method was tested using simulated data and measured data， and experimental results show that the proposed method has better results compared with other gravity data denoising algorithms. In specific， with noise level of 50， in Peak Signal-to-Noise Ratio （PSNR） and Structure SIMilarity （SSIM）， the proposed method improves over 21.8% and 9.3%， respectively， compared to the traditional denoising algorithm BM3D （Block-Matching and 3D filtering）. Compared to the deep learning-based denoising algorithms DnCNN （Denoising Convolutional Neural Network） and MWCNN （Multi-level Wavelet Convolutional Neural Network）， PSNR and SSIM are improved respectively.

Key words: gravity data, wavelet transform, deep learning, residual connectivity, channel attention

摘要：

为降低干扰噪声对重力实测数据的影响，进一步提高重力数据处理精度，提出一种基于多级小波残差网络（MWRNet）的重力数据去噪方法，该方法结合小波变换和神经网络实现对重力数据中噪声分量的去除。首先通过小波变换分解重力数据，再利用神经网络提取噪声，同时引入残差通道注意力（RCA）模块增强网络的噪声提取能力。利用模拟数据和实测数据测试所提方法，实验结果表明：所提方法相较于其他重力数据去噪算法具有更好的效果。在噪声水平为50的实验中，所提方法相较于传统去噪算法三维块匹配算法BM3D（Block-Matching and 3D filtering），在峰值信噪比（PSNR）、结构相似性指数（SSIM）上分别提升了21.8%、9.3%；相较于基于深度学习的去噪算法DnCNN（Denoising Convolutional Neural Network）、MWCNN（Multi-level Wavelet-CNN），PSNR、SSIM也分别有所提升。

关键词: 重力数据, 小波变换, 深度学习, 残差连接, 通道注意力

CLC Number:

TP391

Yali XUE, Zhongmin XU, Shihao LIU. Gravity data denoising method based on multilevel wavelet residual network[J]. Journal of Computer Applications, 2025, 45(10): 3336-3341.

薛雅丽, 徐忠敏, 刘世豪. 基于多级小波残差网络的重力数据去噪方法[J]. 《计算机应用》唯一官方网站, 2025, 45(10): 3336-3341.

Figures/Tables 10

Fig. 1 Schematic diagram of multilevel 2D wavelet transform

Fig. 2 Principles of DWT module and IWT module

Fig. 3 Residual channel attention module

Fig. 4 Overall structure of MWRNet

Tab. 1 Training parameters of MWRNet

项目	内容
优化算法	Adam
初始学习率	10^-3
学习率衰减	CosineAnnealingLR
训练轮数	40
批大小	60
损失函数	MSE

Tab. 2 Average PSNR and SSIM of different combinations of wavelet functions and decomposition layers at noise level σ=25

层数	Haar		Daubechies		Symlet		Coiflet
层数	PSNR/dB	SSIM	PSNR/dB	SSIM	PSNR/dB	SSIM	PSNR/dB	SSIM
3	35.40	0.906 7	35.34	0.910 7	35.01	0.901 2	35.56	0.918 3
2	35.10	0.905 6	35.81	0.920 9	35.45	0.912 1	35.83	0.922 3
1	35.26	0.903 4	35.01	0.898 0	35.66	0.917 2	34.84	0.892 8

Fig. 5 Loss function curve of MWRNet

Tab.3 Average PSNR and SSIM of MWRNet and comparison algorithms at different noise levels σ on test set

算法	$σ$ =15		$σ$ =25		$σ$ =50		$σ$ =75
算法	PSNR/dB	SSIM	PSNR/dB	SSIM	PSNR/dB	SSIM	PSNR/dB	SSIM
IIR滤波	25.36	0.825 3	24.78	0.742 2	21.83	0.541 4	19.35	0.404 2
FIR滤波	34.18	0.927 0	30.85	0.842 1	24.91	0.636 2	21.12	0.479 7
小波分解	35.75	0.928 9	31.51	0.847 6	25.11	0.652 1	21.22	0.501 9
双边滤波	37.18	0.951 6	32.35	0.880 3	26.02	0.717 5	21.74	0.507 8
BM3D	37.48	0.964 3	33.29	0.918 9	26.61	0.794 5	22.27	0.630 9
DnCNN	41.11	0.979 9	37.44	0.956 4	31.97	0.859 9	23.37	0.736 5
MWCNN	41.05	0.982 2	37.50	0.962 0	32.28	0.858 8	23.22	0.790 3
MWRNet	41.41	0.984 6	37.80	0.959 2	32.42	0.868 3	24.00	0.789 3

Tab.3 Average PSNR and SSIM of MWRNet and comparison algorithms at different noise levels σ on test set

算法	$σ$ =15		$σ$ =25		$σ$ =50		$σ$ =75
算法	PSNR/dB	SSIM	PSNR/dB	SSIM	PSNR/dB	SSIM	PSNR/dB	SSIM
IIR滤波	25.36	0.825 3	24.78	0.742 2	21.83	0.541 4	19.35	0.404 2
FIR滤波	34.18	0.927 0	30.85	0.842 1	24.91	0.636 2	21.12	0.479 7
小波分解	35.75	0.928 9	31.51	0.847 6	25.11	0.652 1	21.22	0.501 9
双边滤波	37.18	0.951 6	32.35	0.880 3	26.02	0.717 5	21.74	0.507 8
BM3D	37.48	0.964 3	33.29	0.918 9	26.61	0.794 5	22.27	0.630 9
DnCNN	41.11	0.979 9	37.44	0.956 4	31.97	0.859 9	23.37	0.736 5
MWCNN	41.05	0.982 2	37.50	0.962 0	32.28	0.858 8	23.22	0.790 3
MWRNet	41.41	0.984 6	37.80	0.959 2	32.42	0.868 3	24.00	0.789 3

Fig. 6 Visualization of denoising effect of MWRNet and comparison algorithms at noise level σ=25

Fig. 7 Denoising results of measured data of Vinton Salt Dome

References 19

[1]	曾小牛，李夕海，刘继昊，等. 一种基于改进凸集投影原理的航空重力数据插值与去噪方法［J］. 武汉大学学报（信息科学版）， 2020， 45（10）： 1555-1562.
	ZENG X N， LI X H， LIU J H， et al. Simultaneous interpolation and denoising method for airborne gravity data based on improved projection onto convex sets theory［J］. Geomatics and Information Science of Wuhan University， 2020， 45（10）： 1555-1562.
[2]	LEBLANC G E， MORRIS W A. Denoising of aeromagnetic data via the wavelet transform［J］. Geophysics， 2001， 66（6）： 1793-1804.
[3]	DE OLIVEIRA LYRIO J C S， TENORIO L， LI Y. Efficient automatic denoising of gravity gradiometry data［J］. Geophysics， 2004， 69（3）： 772-782.
[4]	ZHANG D， HUANG D， LU J， et al. Gravity gradient data filtering using translation invariant wavelet［J］. ASEG Extended Abstracts， 2016， 2016（1）： 1-5.
[5]	李宏. 地磁匹配导航航测地磁信号的小波去噪研究［D］. 西安：长安大学， 2023： 33-51.
	LI H. Research on wavelet denoising of aerial geomagnetism in geomagnetic matching navigation［D］. Xi’an： Chang’an University， 2023： 33-51.
[6]	索奎，吕晓春，张贵宾，等. 基于二维小波能量阈值的重磁数据去噪算法［J］. 中国石油大学学报（自然科学版）， 2022， 46（5）： 36-45.
	SUO K， LYU X C， ZHANG G B， et al. Denoising algorithm for gravity and magnetic data based on two-dimensional wavelet energy threshold［J］. Journal of China University of Petroleum （Edition of Natural Science）， 2022， 46（5）： 36-45.
[7]	李冬毅，覃方君，黄春福，等. 基于自寻优小波降噪算法的海洋重力数据滤波［J］. 中国惯性技术学报， 2023， 31（9）： 883-889.
	LI D Y， QIN F J， HUANG C F， et al. Marine gravity data filtering based on self-optimizing wavelet denoising algorithm［J］. Journal of Chinese Inertial Technology， 2023， 31（9）： 883-889.
[8]	WANG J， MENG X， GUO L， et al. A correlation-based approach for determining the threshold value of singular value decomposition filtering for potential field data denoising［J］. Journal of Geophysics and Engineering， 2014， 11（5）： No.055007.
[9]	阳前果. 基于深度学习的重磁数据处理研究［D］. 武汉：中国地质大学， 2021： 30-62.
	YANG Q G. Research on gravity and magnetic data processing based on deep learning［D］. Wuhan： China University of Geosciences， 2021： 30-62.
[10]	黄子炎，王庆宾，赵东明，等. 基于深度残差网络的重力数据去噪重构［J］. 中国惯性技术学报， 2021， 29（4）： 443-450.
	HUANG Z Y， WANG Q B， ZHAO D M， et al. Gravity data denoising and reconstruction based on deep residual network［J］. Journal of Chinese Inertial Technology， 2021， 29（4）： 443-450.
[11]	刘霞，孙英杰. 基于融合残差注意力机制的卷积神经网络地震信号去噪［J］. 吉林大学学报（地球科学版）， 2023， 53（2）： 609-621.
	LIU X， SUN Y J. Seismic signal denoising based on convolutional neural network with residual and attention mechanism［J］. Journal of Jilin University （Earth Science Edition）， 2023， 53（2）： 609-621.
[12]	李从昀，朱亚洲，杨晓，等. 基于Noise-to-Noise自监督学习的地震数据去噪方法［J］. 地球物理学进展， 2023， 38（2）： 662-676.
	LI C Y， ZHU Y Z， YANG X， et al. Seismic data denoising method based on Noise-to-Noise self-supervised learning［J］. Progress in Geophysics， 2023， 38（2）： 662-676.
[13]	赵振聪，饶莹. 基于结构保护去噪神经网络的地震数据随机噪声压制［J］. 地球物理学报， 2024， 67（10）： 3841-3850.
	ZHAO Z C， RAO Y. Seismic random noise suppression based on SP-DnCNN neural network［J］. Chinese Journal of Geophysics， 2024， 67（10）： 3841-3850.
[14]	王洪洲. 基于深度学习的地震勘探数据去噪及速度模型反演技术研究［D］. 长春：吉林大学， 2024： 56-80.
	WANG H Z. Research on deep learning-based seismic exploration data denoising and velocity model inversion［D］. Changchun： Jilin University， 2024： 56-80.
[15]	RONNEBERGER O， FISCHER P， BROX T. U-Net： convolutional networks for biomedical image segmentation［C］// Proceedings of the 2015 International Conference on Medical Image Computing and Computer-Assisted Intervention， LNCS 9351. Cham： Springer， 2015： 234-241.
[16]	高好天，孙宁娜，孙可奕，等. DnCNN和U-Net对地震随机噪声压制的对比分析［J］. 地球物理学进展， 2021， 36（6）： 2441-2453.
	GAO H T， SUN N N， SUN K Y， et al. Comparative analysis of DnCNN and U-Net on suppression of seismic random noise［J］. Progress in Geophysics， 2021， 36（6）： 2441-2453.
[17]	DABOV K， FOI A， KATKOVNIK V， et al. Image denoising by sparse 3-D transform-domain collaborative filtering［J］. IEEE Transactions on Image Processing， 2007， 16（8）： 2080-2095.
[18]	ZHANG K， ZUO W， CHEN Y， et al. Beyond a Gaussian denoiser： residual learning of deep CNN for image denoising［J］. IEEE Transactions on Image Processing， 2017， 26（7）： 3142-3155.
[19]	LIU P， ZHANG H， LIAN W， et al. Multi-level wavelet convolutional neural networks［J］. IEEE Access， 2019， 7： 74973-74985.

Gravity data denoising method based on multilevel wavelet residual network

基于多级小波残差网络的重力数据去噪方法

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