基于压缩感知理论的地震数据降噪方法
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摘要
针对地震数据在采集处理过程中存在的随机噪声,本文从压缩感知的角度,给出了一种地震数据降噪方法.其基本思路是:首先对含有随机噪声地震数据通过离散余弦变换进行稀疏表示,然后选取随机高斯矩阵为测量矩阵,并计算出传感矩阵,在地震数据重构阶段,采用正交匹配追踪算法对地震数据进行重构;通过实验方法对比,本文方法的降噪效果在峰值信噪比、信噪比、均方误差指标上均优于对比方法,证明了本文方法对地震数据中的随机非平稳噪声有较好的压制效果,提高了地震数据的信噪比.
Aiming at the random noise existing in the process of seismic data acquisition and acquisition, this paper presents a method of de-noising seismic data from the perspective of compressed sensing. The basic idea is as follows: Firstly, the seismic data containing random noise is sparsely expressed by discrete cosine transform, then the random Gaussian matrix is chosen as the measurement matrix and the sensing matrix is calculated. In the reconstruction stage of seismic data, orthogonal matching pursuit algorithm the seismic data are reconstructed. By comparing the experimental methods, the noise reduction effect of this method is superior to the comparison method in peak signal-to-noise ratio, signal-to-noise ratio and mean square error index, which proves that the proposed method has better suppression of random non-stationary noise in seismic data. The effect is to improve the signal-to-noise ratio of seismic data.
Aiming at the random noise existing in the process of seismic data acquisition and acquisition, this paper presents a method of de-noising seismic data from the perspective of compressed sensing. The basic idea is as follows: Firstly, the seismic data containing random noise is sparsely expressed by discrete cosine transform, then the random Gaussian matrix is chosen as the measurement matrix and the sensing matrix is calculated. In the reconstruction stage of seismic data, orthogonal matching pursuit algorithm the seismic data are reconstructed. By comparing the experimental methods, the noise reduction effect of this method is superior to the comparison method in peak signal-to-noise ratio, signal-to-noise ratio and mean square error index, which proves that the proposed method has better suppression of random non-stationary noise in seismic data. The effect is to improve the signal-to-noise ratio of seismic data.
引文
Donoho D L.2006.Compressed sensing [J].IEEE Transactions onInformation Theory,52(4):1289-1306.
Fan H Y.2014.Seismic Signal Processing and Application Based on Sparse Representation and Compressed Sensing [Master’s thesis].Chengdu:University of Electronic Science and Technology of China.
Huang S Q.2016.Application of compressed sensing denoising algorithm in random noise suppression in seismic exploration [Master’s thesis].Daqing:Northeast Petroleum University.
Li F L,Chang J,Zhang X Y,et al.2015.Speech Blind Sparse Reconstruction Algorithm Based on Compressive Sensing and Its Application to Noise Reduction [J].Journal of Central South University (Science and Technology) (in Chinese),46(01):164-170.
Li X B.2010.Research on Measurement Matrix Based on Compressed Sensing [Master’s thesis].Beijing:Beijing Jiaotong University.
Luo J S.2016.Research on denoising of TASI data based on compressed sensing [Master’s thesis].Beijing:China University of Geosciences (Beijing).
Lian Q S,Wang X N,Shi B S,et al.2015.Compressed Sensing Based on Multi-analytic Dictionary Learning and Observation Matrix Optimization [J].Chinese Journal of Computers (in Chinese),38(06):1162-1171.
Liu W,Cao S Y,Cui Z.2015.Seismic data denoising based on compressive sensing and TV criterion constraints [J].Petroleum Geophysical Prospecting (in Chinese),54(02):180-187.
LU Q Y.2016.Application of improved EMD in random noise suppression in seismic exploration [Master’s thesis].Changchun:Jilin University.
Song W Q,Zhang Y.2017.Noise suppression of the microseismic data based on the compressive sampling theory [J].Progress in Geophysics (in Chinese),32(04):1636-1642,doi:10.6038/pg20170430.
Tang G.2010.Reconstruction and denoising of seismic data based on compressive sensing and sparse representation [Ph.D.thesis].Beijing:Tsinghua University.
Tian W B,Kang J,Zhang Y,et al.2014.Compressive Sensing Weak Matching Denoising Reconstruction Based on Kalman Filtering [J].Chinese Journal of Electronics (in Chinese),42(06):1061-1067.
Wang Y L,Wen J G.2015.A Multi-measurement De-noising Algorithm Based on Compressed Sensing [J].Microelectronics & Computer (in Chinese),32(07):42- 45.
Zhang B.2013.Research on seismic data denoising based on sparse transform [Master’s thesis].Hangzhou:Zhejiang University.
Zhang J H,Lu N,Tian L Y,et al.2006.Synthetic Review of Seismic Data Denoising Methods [J].Progress in Geophysics (in Chinese),21(02):546-553.
Zhang X P,Hu Z Q,Cheng Z,et al.2014.A method for repairing vibration data based on compressed sensing [J].Acta Physica Sinica,63(20):200506.
Zhang Y X.2013.Research on seismic data denoising method based on digital signal processing in time and space [Ph.D.thesis].Qingdao:China University of Petroleum (East China).
Zhou Y T,Wang L L,Pu Q S.2014.Seismic data reconstruction based on K-singular value decomposition dictionary learning under the framework of compressed sensing [J].Petroleum Geophysical Prospecting (in Chinese),49(04):652- 660.
范弘毅.2014.基于稀疏表示和压缩感知的地震信号处理及应用研究[硕士论文].成都:电子科技大学.
黄胜强.2016.基于压缩感知去噪算法在地震勘探随机噪声压制中的应用[硕士论文].大庆:东北石油大学.
李凤莲,畅江,张雪英,等.2015.基于压缩感知的语音盲稀疏重构算法及其去噪应用[J].中南大学学报(自然科学版),46(01):164-170.
李小波.2010.基于压缩感知的测量矩阵研究[硕士论文].北京:北京交通大学.
练秋生,王小娜,石保顺,等.2015.基于多重解析字典学习和观测矩阵优化的压缩感知[J].计算机学报,38(06):1162-1171.
刘伟,曹思远,崔震.2015.基于压缩感知和TV准则约束的地震资料去噪[J].石油物探,54(02):180-187.
卢秋悦.2016.改进EMD在地震勘探随机噪声压制中的应用[硕士论文].长春:吉林大学.
罗建松.2016.基于压缩感知的TASI数据去噪方法研究[硕士论文].北京:中国地质大学(北京).
宋维琪,张宇.2017.基于压缩感知理论的微地震资料噪声压制[J].地球物理学进展,32(04):1636-1642,doi:10.6038/pg20170430.
唐刚.2010.基于压缩感知和稀疏表示的地震数据重建与去噪[博士论文].北京:清华大学.
田文飚,康健,张洋,等.2014.基于卡尔曼滤波的压缩感知弱匹配去噪重构[J].电子学报,42(06):1061-1067.
王玉林,文建国.2015.一种基于压缩感知的多重测量去噪算法[J].微电子学与计算机,32(07):42- 45.
张博.2013.基于稀疏变换的地震数据去噪方法研究[硕士论文].杭州:浙江大学.
张军华,吕宁,田连玉,等.2006.地震资料去噪方法技术综合评述[J].地球物理学进展,21(02):546-553,doi:10.3969/j.issn.1004-2903.2006.02.033.
张银雪.2013.基于时空域数字信号处理的地震资料降噪方法研究[博士论文].青岛:中国石油大学(华东).
张新鹏,胡茑庆,程哲,等.2014.基于压缩感知的振动数据修复方法[J].物理学报,63(20):200506.
周亚同,王丽莉,蒲青山.2014.压缩感知框架下基于K-奇异值分解字典学习的地震数据重建[J].石油地球物理勘探,49(04):652- 660.
Fan H Y.2014.Seismic Signal Processing and Application Based on Sparse Representation and Compressed Sensing [Master’s thesis].Chengdu:University of Electronic Science and Technology of China.
Huang S Q.2016.Application of compressed sensing denoising algorithm in random noise suppression in seismic exploration [Master’s thesis].Daqing:Northeast Petroleum University.
Li F L,Chang J,Zhang X Y,et al.2015.Speech Blind Sparse Reconstruction Algorithm Based on Compressive Sensing and Its Application to Noise Reduction [J].Journal of Central South University (Science and Technology) (in Chinese),46(01):164-170.
Li X B.2010.Research on Measurement Matrix Based on Compressed Sensing [Master’s thesis].Beijing:Beijing Jiaotong University.
Luo J S.2016.Research on denoising of TASI data based on compressed sensing [Master’s thesis].Beijing:China University of Geosciences (Beijing).
Lian Q S,Wang X N,Shi B S,et al.2015.Compressed Sensing Based on Multi-analytic Dictionary Learning and Observation Matrix Optimization [J].Chinese Journal of Computers (in Chinese),38(06):1162-1171.
Liu W,Cao S Y,Cui Z.2015.Seismic data denoising based on compressive sensing and TV criterion constraints [J].Petroleum Geophysical Prospecting (in Chinese),54(02):180-187.
LU Q Y.2016.Application of improved EMD in random noise suppression in seismic exploration [Master’s thesis].Changchun:Jilin University.
Song W Q,Zhang Y.2017.Noise suppression of the microseismic data based on the compressive sampling theory [J].Progress in Geophysics (in Chinese),32(04):1636-1642,doi:10.6038/pg20170430.
Tang G.2010.Reconstruction and denoising of seismic data based on compressive sensing and sparse representation [Ph.D.thesis].Beijing:Tsinghua University.
Tian W B,Kang J,Zhang Y,et al.2014.Compressive Sensing Weak Matching Denoising Reconstruction Based on Kalman Filtering [J].Chinese Journal of Electronics (in Chinese),42(06):1061-1067.
Wang Y L,Wen J G.2015.A Multi-measurement De-noising Algorithm Based on Compressed Sensing [J].Microelectronics & Computer (in Chinese),32(07):42- 45.
Zhang B.2013.Research on seismic data denoising based on sparse transform [Master’s thesis].Hangzhou:Zhejiang University.
Zhang J H,Lu N,Tian L Y,et al.2006.Synthetic Review of Seismic Data Denoising Methods [J].Progress in Geophysics (in Chinese),21(02):546-553.
Zhang X P,Hu Z Q,Cheng Z,et al.2014.A method for repairing vibration data based on compressed sensing [J].Acta Physica Sinica,63(20):200506.
Zhang Y X.2013.Research on seismic data denoising method based on digital signal processing in time and space [Ph.D.thesis].Qingdao:China University of Petroleum (East China).
Zhou Y T,Wang L L,Pu Q S.2014.Seismic data reconstruction based on K-singular value decomposition dictionary learning under the framework of compressed sensing [J].Petroleum Geophysical Prospecting (in Chinese),49(04):652- 660.
范弘毅.2014.基于稀疏表示和压缩感知的地震信号处理及应用研究[硕士论文].成都:电子科技大学.
黄胜强.2016.基于压缩感知去噪算法在地震勘探随机噪声压制中的应用[硕士论文].大庆:东北石油大学.
李凤莲,畅江,张雪英,等.2015.基于压缩感知的语音盲稀疏重构算法及其去噪应用[J].中南大学学报(自然科学版),46(01):164-170.
李小波.2010.基于压缩感知的测量矩阵研究[硕士论文].北京:北京交通大学.
练秋生,王小娜,石保顺,等.2015.基于多重解析字典学习和观测矩阵优化的压缩感知[J].计算机学报,38(06):1162-1171.
刘伟,曹思远,崔震.2015.基于压缩感知和TV准则约束的地震资料去噪[J].石油物探,54(02):180-187.
卢秋悦.2016.改进EMD在地震勘探随机噪声压制中的应用[硕士论文].长春:吉林大学.
罗建松.2016.基于压缩感知的TASI数据去噪方法研究[硕士论文].北京:中国地质大学(北京).
宋维琪,张宇.2017.基于压缩感知理论的微地震资料噪声压制[J].地球物理学进展,32(04):1636-1642,doi:10.6038/pg20170430.
唐刚.2010.基于压缩感知和稀疏表示的地震数据重建与去噪[博士论文].北京:清华大学.
田文飚,康健,张洋,等.2014.基于卡尔曼滤波的压缩感知弱匹配去噪重构[J].电子学报,42(06):1061-1067.
王玉林,文建国.2015.一种基于压缩感知的多重测量去噪算法[J].微电子学与计算机,32(07):42- 45.
张博.2013.基于稀疏变换的地震数据去噪方法研究[硕士论文].杭州:浙江大学.
张军华,吕宁,田连玉,等.2006.地震资料去噪方法技术综合评述[J].地球物理学进展,21(02):546-553,doi:10.3969/j.issn.1004-2903.2006.02.033.
张银雪.2013.基于时空域数字信号处理的地震资料降噪方法研究[博士论文].青岛:中国石油大学(华东).
张新鹏,胡茑庆,程哲,等.2014.基于压缩感知的振动数据修复方法[J].物理学报,63(20):200506.
周亚同,王丽莉,蒲青山.2014.压缩感知框架下基于K-奇异值分解字典学习的地震数据重建[J].石油地球物理勘探,49(04):652- 660.