基于交叠组稀疏广义全变分的地震信号随机噪声衰减

doi:10.13810/j.cnki.issn.1000-7210.2019.01.004

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摘要广义全变分方法能较有效去除地震信号随机噪声。本文将交叠组稀疏收敛技术引入广义全变分模型，提出一种改进的广义全变分去噪方法。该方法更充分地挖掘并利用了图像一阶梯度和二阶梯度的结构稀疏的先验知识，从而获得比常规广义全变分更好的去噪效果。针对构建的改进模型，基于交替乘子迭代法框架，将多约束问题转化为去耦合的若干子问题，并引入傅里叶变换技术以提高算法运行效率。针对地震信号进行的各类全变分去噪方法的对比实验结果显示，本文方法的去噪性能相比于常规广义全变分方法具有较大提升，尤其对重噪声污染像素点具有更好的去噪效果。

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关键词 ：广义全变分, 交替乘子迭代法, 交叠组稀疏, 地震去噪, 快速傅里叶变换

Abstract：The total generalized variation (TGV) denoising is a conventional way to suppress random noise in seismic data.This paper introduces the overlapping group sparsity into the TGV model and proposes an improved TGV denoising model.The proposed model explores the structural property of the first and second orders' image differential information.As a result,the proposed model performs better than the TGV model.We adopt the alternating direction method of multipliers (ADMM) to solve the proposed model.In the framework of ADMM,the multi-constrained problem is divided into several sub-problems that are easier to be solved.Furthermore,to improve the efficiency of the algorithm,we use the fast Fourier transform.Experiments verify that the proposed method outperforms than conventional TGV,especially for removing strong noise.

Key words： total generalized variation alternating direction method of multipliers (ADMM) overlapping group sparsity seismic denoising fast Fourier transform

收稿日期: 2018-04-16

PACS:

P631

基金资助:本项研究受国家自然科学基金项目“结合背景特性与目标正演的稀疏动态反演空间红外弱小目标检测方法”（61571096）、“复杂地震信号分数域频谱成像理论及应用研究”（41274127）、福建省教育厅中青年教师教育科研项目“稀疏时频分析算法及其在异常频谱检测的应用”（JAT170352）、福建省重大教改项目“人工智能视角下的应用型人才培养模式创新和改革”（FBJG20180015）和广东省数字信号与图像处理技术重点实验室开放课题“基于凸优化理论的稀疏时频成像方法研究”（2017GDDSIPL-01）等联合资助。

通讯作者: 彭真明,四川省成都市成华区建设北路二段4号电子科技大学信息与通信工程学院,610054。Email:zmpeng@uestc.edu.cn E-mail: zmpeng@uestc.edu.cn

作者简介: 陈颖频,博士研究生,1986年生;2009年获福州大学电子科学与技术专业学士学位,2013年获电子科技大学信号与信息处理专业硕士学位;已在SCI、EI数据库收录期刊上发表论文十余篇;现在闽南师范大学从事压缩感知、时频分析技术、凸优化理论等方面的教研,同时在电子科技大学攻读信号与信息处理专业博士学位。

引用本文:

陈颖频, 彭真明, 李美惠, 喻飞. 基于交叠组稀疏广义全变分的地震信号随机噪声衰减[J]. 石油地球物理勘探, 2019, 54(1): 24-35,44. CHEN Yingpin, PENG Zhenming, LI Meihui, YU Fei. Random noise suppression based on the improved total generalized variation with overlapping group sparsity. Oil Geophysical Prospecting, 2019, 54(1): 24-35,44.

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