Time-varying wavelet estimation based on improved online dictionary learning
Kong Dehui1,2, Peng Zhenming1,2
1. School of Optoelectronic Information, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China;
2. Information Geoscience Research Center, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China
Abstract：In order to obtain a mixed phase wavelet which is fit with real state, we introduce a time-varying wavelet estimation method based on online dictionary learning. The time-varying wavelet estimation is transformed into an online dictionary learning problem where the redundant dictionary is adaptively updated through its online learning process. Each atom in the dictionary represents a component of the varying wavelet. Its accurate approximatation is realized by a line combination of those atoms. Online dictionary learning uses flexibly the training data, updates the atoms in the dictionary, and enhances the adaptability of the dictionary. According to characteristics of seismic data, residuals between the training data and sparse representation are filtered which improves the online dictionary learning and reduces the sensitivity to noise. In noise free and noisy synthetic data tests, the results show the validity of the proposed method and its robustness against noise. Wavelet estimation on field data, Wiener filtering deconvolution sections and spectral analysis are also obtained. The outcome shows that the proposed method widen frequency band without noise energy increase, which provides an alternative way to estimate time-varying wavelet.
Yue Bibo, Peng Zhenming, Hong Yugang et al. Wavelet inversion of pre-stack seismic angle-gather based on particle swarm optimization algorithm.Chinese Journal of Geophysics, 2009, 52(12):3116-3123.
[4]
Zheng J,Peng S P,Liu M C et al. A novel seismic wavelet estimation method.Journal of Applied Geophysics, 2013,90(1):92-95.
[5]
Yue B B,Peng Z M,Zhang Q H.Seismic wavelet estimation using covariation approach. IEEE Transactions on Geoscience and Remote Sensing,2014,52(12):7495-7503.
Dai Yongshou, Wang Xiaobo, Ding Jinjie et al. Time-variant wavelet estimation based on adaptive segmentation.OGP,2015,50(4):607-612.
[7]
Chen G,Needell D.Compressed sensing and dictionary learning.Chapter 15 in Finite Frame Theory. Proceedings of Symposia in Applied American Mathmatical Society,2016,73:201-204.
[8]
Engan K,Aase S O,Hakon Husoy J.Method of optimal directions for frame design.Proceedings of the 1999 IEEE International Conference on Acoustics,Speech,and Signal Processing,Phoenix,AZ,USA,1999, 2443-2446.
[9]
Aharon M,Elad M,Bruckstein A.K-SVD:An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Transactions on Signal Processing,2006,54(11):4311-4322.
[10]
Mairal J,Bach F,Ponce J et al.Online learning for matrix factorization and sparse coding.The Journal of Machine Learning Research,2010, 11(1):19-60.
[11]
Skretting K,Engan K.Recursive least squares dictionary learning algorithm. IEEE Transactions on Signal Processing,2010,58(4):2121-2130.
[12]
Naderahmadian Y,Tinati M A,Beheshti S.Generalized adaptive weighted recursive least squares dictionary learning.Signal Processing,2016,118(1):89-96.
[13]
Tang Gang,Ma Jianwei,Yang Huizhu.Seismic data denoising based on learning-type overcomplete dictionaries. Applied Geophysics,2012,9(1):27-32.
[14]
Rebollo N L,Lowe D.Optimized orthogonal mat-ching pursuit approach. IEEE Signal Processing Letters, 2002,9(4):137-140.
Dai Shuanghe, Chen Zhigang, Yu Jingbo et al. Application of multi-wavelet decomposition and reconstruction technique in reservoir characterization in TKT-NGS oilfield, Algeria. OGP,2011,46(1):103-109.
[17]
Berkhout A.Least-squares inverse filtering and wavelet deconvolution.Geophysics,1977, 42(7):1369-1383.
