基于波原子变换的三维地震信号盲去噪
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摘要
基于波原子变换的三维地震信号盲去噪算法,利用基于块的噪声估计算法估计信号噪声,采用循环平移处理信号并进行波原子变换,利用估计的噪声标准差按不同尺度分层设置阈值并进行修正,再采用改进的阈值函数处理波原子变换系数,进行波原子反变换与逆循环平移,得到去噪后三维地震信号。对含噪的合成与实际地震信号去噪,并与小波、双树复小波、曲波及传统波原子变换的去噪结果对比;结果表明,该算法较其它对比算法有明显优势,且随含噪量的增加,去噪优势愈加明显。从输出信噪比、均方误差以及峰值信噪比等评价指标可知,基于波原子变换的三维地震信号盲去噪算法去噪效果最佳,其次为传统波原子变换算法,然后为曲波变换与双树复小波变换算法,传统小波变换算法的去噪效果最差。
A blind 3 D seismic signal denoising algorithm based on the wave atom transform was proposed. Firstly, the patch-based noise estimation algorithm was used to estimate the noise, then the seismic signal was processed by cycle-spinning and the wave atom transform. The threshold was set and corrected according to different scales by noise standard deviation, and the improved threshold function was used to deal with the transformed coefficients. Finally, the inverse wave atom transform and cycle-spinning were performed to obtain the denoised signal. The synthetic and field seismic signal with noise were denoised and compared with wavelet, dual-tree complex wavelet, curvelet and traditional wave atom transform. The results show that the proposed algorithm has obvious advantages. With the increase of noise, the denoising advantage becomes more obvious. From the evaluation indicators including output signal to noise ratio, mean square error and peak signal to noise ratio can be analyzed, the best denoising algorithm is the blind 3 D seismic signal denoising algorithm based on wave atom transform, followed by the traditional wave atom transform algorithm, then the curvelet transform algorithm and dual-tree complex wavelet transform algorithm, the wavelet transform algorithm performs worst.
A blind 3 D seismic signal denoising algorithm based on the wave atom transform was proposed. Firstly, the patch-based noise estimation algorithm was used to estimate the noise, then the seismic signal was processed by cycle-spinning and the wave atom transform. The threshold was set and corrected according to different scales by noise standard deviation, and the improved threshold function was used to deal with the transformed coefficients. Finally, the inverse wave atom transform and cycle-spinning were performed to obtain the denoised signal. The synthetic and field seismic signal with noise were denoised and compared with wavelet, dual-tree complex wavelet, curvelet and traditional wave atom transform. The results show that the proposed algorithm has obvious advantages. With the increase of noise, the denoising advantage becomes more obvious. From the evaluation indicators including output signal to noise ratio, mean square error and peak signal to noise ratio can be analyzed, the best denoising algorithm is the blind 3 D seismic signal denoising algorithm based on wave atom transform, followed by the traditional wave atom transform algorithm, then the curvelet transform algorithm and dual-tree complex wavelet transform algorithm, the wavelet transform algorithm performs worst.
引文
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[2]LEBRUN M,COLOM M,MOREL J M.The noise clinic:a blind image denoising algorithm[J].Image Processing on Line,2015,5(1):1-54.
[3]ZHU X,MILANFAR P.Automatic parameter selection for denoising algorithms using a no-reference measure of image content[J].IEEE Transactions on Image Processing,2010,19(12):3116-3132.
[4]SCHMIDT U,SCHELTEN K,ROTH S.Bayesian deblurring with integrated noise estimation[J].IEEE Conference on Computer Vision&Pattern Recognition,2011,32(14):2625-2632.
[5]傅鹏,孙权森,纪则轩.结合分形理论和自适应图像块划分的遥感图像噪声估计[J].测绘学报,2015,44(11):1235-1245.FU Peng,SUN Quansen,JI Zexuan.Noise estimation from remote sensing images by fractal theory and adaptive image block division[J].Acta Geodaetica et Cartographica Sinica,2015,44(11):1235-1245.
[6]林旭,罗志才.一种新的卫星钟差Kalman滤波噪声协方差估计方法[J].物理学报,2015,64(8):18-23.LIN Xu,LUO Zhicai.A new noise covariance matrix estimation method of Kalman filter for satellite clock errors[J].Acta Physica Sinica,2015,64(8):18-23.
[7]ZORAN D,WEISS Y.Scale invariance and noise in natural images[C]//IEEE,International Conference on Computer Vision.Kyoto:IEEE,2009.
[8]LIU X,TANAKA M,OKUTOMI M.Single-image noise level estimation for blind denoising[J].IEEE Transactions on Image Processing,2013,22(12):5226-5237.
[9]王宏强,尚春阳,高瑞鹏,等.基于小波系数变换的小波阈值去噪算法改进[J].振动与冲击,2011,30(10):165-168.WANG Hongqiang,SHANG Chunyang,GAO Ruipeng,et al.An improvement of wavelet shrinkage denoising via wavelet coefficient transformation[J].Journal of Vibration and Shock,2011,30(10):165-168.
[10]CHEN G Y,KGL B.Image denoising with complex ridgelets[J].Pattern Recognition,2007,40(2):578-585.
[11]纪建,许双星,李晓.基于形态成分分析和Contourlet变换的自适应阈值图像去噪方法[J].模式识别与人工智能,2014,27(6):561-568.JI Jian,XU Shuangxing,LI Xiao.An adaptive thresholding image denoising method based on morphological component analysis and contourlet transform[J].Pattern Recognition and Artificial Intelligence,2014,27(6):561-568.
[12]BHADAURIA H S,DEWAL M L.Medical image denoising using adaptive fusion of curvelet transform and total variation[J].Computers&Electrical Engineering,2013,39(5):1451-1460.
[13]HADDAD Z,BEGHDADI A,SERIR A,et al.Wave atoms based compression method for fingerprint images[J].Pattern Recognition,2013,46(9):2450-2464.
[14]ZHANG W Q,SONG Y M,FENG J Q.A new image denoising method based on wave atoms and cycle spinning[J].Journal of Software,2014,9(1):310-313.
[15]杨宁,贺振华,黄德济.基于系数相关性阈值的波原子域叠前地震资料信噪分离方法[J].石油地球物理勘探,2011,46(1):53-57.YANG Ning,HE Zhenhua,HUANG Deji.Signal and noise separation method for pre-stack seismic data in wave atomic domain based on coefficient correlation threshold[J].Oil Geophysical Prospecting,2011,46(1):53-57.
[16]DEMANET L,YING L.Wave atoms and sparsity of oscillatory patterns[J].Applied&Computational Harmonic Analysis,2007,23(3):368-387.
[17]宋宜美,宋国乡.结合波原子和Cycle Spinning的图像去噪[J].西安电子科技大学学报(自然科学版),2010,37(2):300-304.SONG Yimei,SONG Guoxiang.Image denoising based on wave atoms and cycle spinning[J].Journal of Xidian University(Science),2010,37(2):300-304.
[18]COIFMAN R R,DONOHO D L.Translation-invariant denoising[J].Lecture Notes in Statistics,1995,103(2):125-150.
[19]DONOHO D L,JOHNSTONE I M.Taylor&Francis online:adapting to unknown smoothness via wavelet shrinkage[J].Journal of the American Statistical Association,1995,90(432):1200-1224.
[20]LU J Y,HONG L,DONG Y,et al.A new wavelet threshold function and denoising application[J].Mathematical Problems in Engineering,2016(3):1-8.