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No AccessGEOPHYSICSVolume 82, Issue 6

Data-driven multitask sparse dictionary learning for noise attenuation of 3D seismic data

Authors:
https://doi.org/10.1190/geo2017-0084.1

ABSTRACT

Representation of a signal in a sparse way is a useful and popular methodology in signal-processing applications. Among several widely used sparse transforms, dictionary learning (DL) algorithms achieve most attention due to their ability in making data-driven nonanalytical (nonfixed) atoms. Various DL methods are well-established in seismic data processing due to the inherent low-rank property of this kind of data. We have introduced a novel data-driven 3D DL algorithm that is extended from the 2D nonnegative DL scheme via the multitasking strategy for random noise attenuation of seismic data. In addition to providing parts-based learning, we exploit nonnegativity constraint to induce sparsity on the data transformation and reduce the space of the solution and, consequently, the computational cost. In 3D data, we consider each slice as a task. Whereas 3D seismic data exhibit high correlation between slices, a multitask learning approach is used to enhance the performance of the method by sharing a common sparse coefficient matrix for the whole related tasks of the data. Basically, in the learning process, each task can help other tasks to learn better and thus a sparser representation is obtained. Furthermore, different from other DL methods that use a limited random number of patches to learn a dictionary, the proposed algorithm can take the whole data information into account with a reasonable time cost and thus can obtain an efficient and effective denoising performance. We have applied the method on synthetic and real 3D data, which demonstrated superior performance in random noise attenuation when compared with state-of-the-art denoising methods such as MSSA, BM4D, and FXY predictive filtering, especially in amplitude and continuity preservation in low signal-to-noise ratio cases and fault zones.

REFERENCES

  • Abma, R., and J. Claerbout, 1995, Lateral prediction for noise attenuation by tx and fx techniques: Geophysics, 60, 1887–1896, doi: 10.1190/1.1443920.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Anvari, R., M. A. N. Siahsar, S. Gholtashi, A. R. Kahoo, and M. Mohammadi, 2017, Seismic random noise attenuation using synchrosqueezed wavelet transform and low-rank signal matrix approximation: IEEE Transactions on Geoscience and Remote Sensing, 1–8, doi: 10.1109/TGRS.2017.2730228.
    Web of ScienceGoogle Scholar
  • Badea, L., 2008, Extracting gene expression profiles common to colon and pancreatic adenocarcinoma using simultaneous nonnegative matrix factorization: Pacific Symposium on Biocomputing, Citeseer, 279–290.
    Google Scholar
  • Beckouche, S., and J. Ma, 2014, Simultaneous dictionary learning and denoising for seismic data: Geophysics, 79, no. 3, A27–A31, doi: 10.1190/geo2013-0382.1.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Bioucas-Dias, J. M., and J. M. P. Nascimento, 2008, Hyperspectral subspace identification: IEEE Transactions on Geoscience and Remote Sensing, 46, 2435–2445, doi: 10.1109/TGRS.2008.918089.IGRSD20196-2892
    Web of ScienceGoogle Scholar
  • Bonar, D., and M. Sacchi, 2012, Denoising seismic data using the nonlocal means algorithm: Geophysics, 77, no. 1, A5–A8, doi: 10.1190/geo2011-0235.1.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Boßmann, F., and J. Ma, 2015, Asymmetric chirplet transform for sparse representation of seismic data: Geophysics, 80, no. 6, WD89–WD100, doi: 10.1190/geo2015-0063.1.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Chen, K., and M. D. Sacchi, 2014, Robust reduced-rank filtering for erratic seismic noise attenuation: Geophysics, 80, no. 1, V1–V11, doi: 10.1190/geo2014-0116.1.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Chen, Y., 2015, Iterative deblending with multiple constraints based on shaping regularization: IEEE Geoscience and Remote Sensing Letters, 12, 2247–2251, doi: 10.1109/LGRS.2015.2463815.
    Web of ScienceGoogle Scholar
  • Chen, Y., 2017, Fast dictionary learning for random noise attenuation of multidimensional seismic data: Geophysical Journal International, 209, 21–31, doi: 10.1093/gji/ggw492.GJINEA0956-540X
    Web of ScienceGoogle Scholar
  • Chen, Y., and S. Fomel, 2015a, EMD-seislet transform: 85th Annual International Meeting, SEG, Expanded Abstracts, 4775–4778.
    Google Scholar
  • Chen, Y., and S. Fomel, 2015b, Random noise attenuation using local signal-and-noise orthogonalization: Geophysics, 80, no. 6, WD1–WD9, doi: 10.1190/geo2014-0227.1.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Chen, Y., S. Fomel, and J. Hu, 2014, Iterative deblending of simultaneous-source seismic data using seislet-domain shaping regularization: Geophysics, 79, no. 5, V179–V189, doi: 10.1190/geo2013-0449.1.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Chen, Y., and J. Ma, 2014, Random noise attenuation by f-x empirical-mode decomposition predictive filtering: Geophysics, 79, no. 3, V81–V91, doi: 10.1190/geo2013-0080.1.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Chen, Y., J. Ma, and S. Fomel, 2016b, Double-sparsity dictionary for seismic noise attenuation: Geophysics, 81, no. 2, V103–V116, doi: 10.1190/geo2014-0525.1.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Chen, Y., D. Zhang, Z. Jin, X. Chen, S. Zu, W. Huang, and S. Gan, 2016a, Simultaneous denoising and reconstruction of 5-D seismic data via damped rank-reduction method: Geophysical Journal International, 206, 1695–1717, doi: 10.1093/gji/ggw230.GJINEA0956-540X
    Web of ScienceGoogle Scholar
  • Daubechies, I., M. Defrise, and C. De Mol, 2004, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint: Communications on Pure and Applied Mathematics, 57, 1413–1457, doi: 10.1002/(ISSN)1097-0312.CPMAMV0010-3640
    Web of ScienceGoogle Scholar
  • Ding, C., C. Xu, and D. Tao, 2015, Multi-task pose-invariant face recognition: IEEE Transactions on Image Processing, 24, 980–993, doi: 10.1109/TIP.2015.2390959.IIPRE41057-7149
    Web of ScienceGoogle Scholar
  • Ding, C. H., T. Li, and M. I. Jordan, 2010, Convex and semi-nonnegative matrix factorizations: IEEE Transactions on Pattern Analysis and Machine Intelligence, 32, 45–55, doi: 10.1109/TPAMI.2008.277.ITPIDJ0162-8828
    Web of ScienceGoogle Scholar
  • Dong, W., X. Li, L. Zhang, and G. Shi, 2011, Sparsity-based image denoising via dictionary learning and structural clustering:IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 457–464.
    Google Scholar
  • Durrani, T. S., and D. Bisset, 1984, The Radon transform and its properties: Geophysics, 49, 1180–1187, doi: 10.1190/1.1441747.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Elad, M., and M. Aharon, 2006, Image denoising via sparse and redundant representations over learned dictionaries: IEEE Transactions on Image Processing, 15, 3736–3745, doi: 10.1109/TIP.2006.881969.
    Web of ScienceGoogle Scholar
  • Engan, K., S. O. Aase, and J. H. Husoy, 1999, Method of optimal directions for frame design: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 2443–2446.
    Google Scholar
  • Fomel, S., and Y. Liu, 2010, Seislet transform and seislet frame: Geophysics, 75, no. 3, V25–V38, doi: 10.1190/1.3380591.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Gillis, N., and F. Glineur, 2012, Accelerated multiplicative updates and hierarchical ALS algorithms for nonnegative matrix factorization: Neural Computation, 24, 1085–1105, doi: 10.1162/NECO_a_00256.NEUCEB0899-7667
    Web of ScienceGoogle Scholar
  • Gülünay, N., 2000, Noncausal spatial prediction filtering for random noise reduction on 3-D poststack data: Geophysics, 65, 1641–1653, doi: 10.1190/1.1444852.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Herrmann, F. J., U. Böniger, and D. J. E. Verschuur, 2007, Non-linear primary-multiple separation with directional curvelet frames: Geophysical Journal International, 170, 781–799, doi: 10.1111/j.1365-246X.2007.03360.x.GJINEA0956-540X
    Web of ScienceGoogle Scholar
  • Herrmann, F. J., and G. Hennenfent, 2008, Non-parametric seismic data recovery with curvelet frames: Geophysical Journal International, 173, 233–248, doi: 10.1111/j.1365-246X.2007.03698.x.GJINEA0956-540X
    Web of ScienceGoogle Scholar
  • Huang, W., R. Wang, X. Chen, and Y. Chen, 2017a, Double least-squares projections method for signal estimation: IEEE Transactions on Geoscience and Remote Sensing, 55, 4111–4129, doi: 10.1109/TGRS.2017.2688420.IGRSD20196-2892
    Web of ScienceGoogle Scholar
  • Huang, W., R. Wang, Y. Chen, H. Li, and S. Gan, 2016, Damped multichannel singular spectrum analysis for 3D random noise attenuation: Geophysics, 81, no. 4, V261–V270, doi: 10.1190/geo2015-0264.1.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Huang, W., R. Wang, Y. Yuan, S. Gan, and Y. Chen, 2017b, Signal extraction using randomized-order multichannel singular spectrum analysis: Geophysics, 82, no. 2, V69–V84, doi: 10.1190/geo2015-0708.1.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Ibrahim, A., and M. D. Sacchi, 2014, Simultaneous source separation using a robust Radon transform: Geophysics, 79, no. 1, V1–V11, doi: 10.1190/geo2013-0168.1.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Kim, H., and H. Park, 2007, Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis: Bioinformatics, 23, 1495–1502, doi: 10.1093/bioinformatics/btm134.BOINFP1367-4803
    Web of ScienceGoogle Scholar
  • Kong, D., and Z. Peng, 2015, Seismic random noise attenuation using shearlet and total generalized variation: Journal of Geophysics and Engineering, 12, 1024–1035, doi: 10.1088/1742-2132/12/6/1024.
    Web of ScienceGoogle Scholar
  • Kong, D., Z. Peng, Y. He, and H. Fan, 2016, Seismic random noise attenuation using directional total variation in the shearlet domain: Journal of Seismic Exploration, 25, 321–338.
    Web of ScienceGoogle Scholar
  • Kumar, V., and F. J. Herrmann, 2009, Incoherent noise suppression with curvelet-domain sparsity: 79th Annual International Meeting, SEG, Expanded Abstracts, 3356–3360.
    Google Scholar
  • Lee, D. D., and H. S. Seung, 1999, Learning the parts of objects by non-negative matrix factorization: Nature, 401, 788–791, doi: 10.1038/44565.
    Web of ScienceGoogle Scholar
  • Lee, D. D., and H. S. Seung, 2001, Algorithms for non-negative matrix factorization, in M. I. JordanY. LeCunS. A. Solla, eds., Advances in neural information processing systems: MIT Press: 556–562.
    Google Scholar
  • Lee, K., S. Tak, and J. C. Ye, 2011, A data-driven sparse GLM for fMRI analysis using sparse dictionary learning with MDL criterion: IEEE Transactions on Medical Imaging, 30, 1079–1089, doi: 10.1109/TMI.2010.2097275.ITMID40278-0062
    Web of ScienceGoogle Scholar
  • Li, Y., and A. Ngom, 2012, A new kernel non-negative matrix factorization and its application in microarray data analysis: IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB), 371–378.
    Google Scholar
  • Li, Y., and A. Ngom, 2014, Versatile sparse matrix factorization: Theory and applications: Neurocomputing, 145, 23–29, doi: 10.1016/j.neucom.2014.05.076.NRCGEO0925-2312
    Web of ScienceGoogle Scholar
  • Liu, C., D. Wang, B. Hu, and T. Wang, 2016a, Seismic deconvolution with shearlet sparsity constrained inversion: Journal of Applied Geophysics, 25, 433–445.JAGPEA0926-9851
    Google Scholar
  • Liu, G., X. Chen, J. Du, and K. Wu, 2012, Random noise attenuation using f-x regularized nonstationary autoregression: Geophysics, 77, no. 2, V61–V69, doi: 10.1190/geo2011-0117.1.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Liu, T., Y. Si, D. Wen, M. Zang, and L. Lang, 2016b, Dictionary learning for VQ feature extraction in ECG beats classification: Expert Systems with Applications, 53, 129–137, doi: 10.1016/j.eswa.2016.01.031.ESAPEH0957-4174
    Web of ScienceGoogle Scholar
  • Liu, Y., S. Fomel, and C. Liu, 2015, Signal and noise separation in prestack seismic data using velocity-dependent seislet transform: Geophysics, 80, no. 6, WD117–WD128, doi: 10.1190/geo2014-0234.1.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Liu, Y., N. Liu, and C. Liu, 2014, Adaptive prediction filtering in txy domain for random noise attenuation using regularized nonstationary autoregression: Geophysics, 80, no. 1, V13–V21, doi: 10.1190/geo2014-0011.1.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Maggioni, M., V. Katkovnik, K. Egiazarian, and A. Foi, 2013, A nonlocal transform-domain filter for volumetric data denoising and reconstruction: IEEE Transactions on Image Processing, 22, 119–133, doi: 10.1109/TIP.2012.2210725.
    Web of ScienceGoogle Scholar
  • Meinshausen, N., and B. Yu, 2009, Lasso-type recovery of sparse representations for high-dimensional data: The Annals of Statistics, 37, 246–270, doi: 10.1214/07-AOS582.
    Web of ScienceGoogle Scholar
  • Mousavi, S. M., S. P. Horton, C. A. Langston, and B. Samei, 2016b, Seismic features and automatic discrimination of deep and shallow induced-microearthquakes using neural network and logistic regression: Geophysical Journal International, 207, 29–46, doi: 10.1093/gji/ggw258.GJINEA0956-540X
    Web of ScienceGoogle Scholar
  • Mousavi, S. M., and C. A. Langston, 2016a, Adaptive noise estimation and suppression for improving microseismic event detection: Journal of Applied Geophysics, 132, 116–124, doi: 10.1016/j.jappgeo.2016.06.008.JAGPEA0926-9851
    Web of ScienceGoogle Scholar
  • Mousavi, S. M., and C. A. Langston, 2016b, Hybrid seismic denoising using higher‐order statistics and improved wavelet block thresholding: Bulletin of the Seismological Society of America, 106, 1380–1393, doi: 10.1785/0120150345.BSSAAP0037-1106
    Web of ScienceGoogle Scholar
  • Mousavi, S. M., C. A. Langston, and S. P. Horton, 2016a, Automatic microseismic denoising and onset detection using the synchrosqueezed continuous wavelet transform: Geophysics, 81, no. 4, V341–V355, doi: 10.1190/geo2015-0598.1.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Nazari Siahsar, M. A., S. Gholtashi, V. Abolghasemi, and Y. Chen, 2017b, Simultaneous denoising and interpolation of 2D seismic data using data-driven non-negative dictionary learning: Signal Processing, 141, 309–321, doi: 10.1016/j.sigpro.2017.06.017.SPRODR0165-1684
    Web of ScienceGoogle Scholar
  • Nazari Siahsar, M. A., S. Gholtashi, A. R. Kahoo, H. Marvi, and A. Ahmadifard, 2016, Sparse time-frequency representation for seismic noise reduction using low-rank and sparse decomposition: Geophysics, 81, no. 2, V117–V124, doi: 10.1190/geo2015-0341.1.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Nazari Siahsar, M. A., S. Gholtashi, E. Olyaei Torshizi, W. Chen, and Y. Chen, 2017a, Simultaneous denoising and interpolation of 3D seismic data via damped data-driven optimal singular value shrinkage: IEEE Geoscience and Remote Sensing Letters, 14, 1086–1090, doi: 10.1109/LGRS.2017.2697942.
    Web of ScienceGoogle Scholar
  • Oropeza, V., and M. Sacchi, 2011, Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis: Geophysics, 76, no. 3, V25–V32, doi: 10.1190/1.3552706.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Qu, S., H. Zhou, R. Liu, Y. Chen, S. Zu, S. Yu, J. Yuan, and Y. Yang, 2016, Deblending of simultaneous-source seismic data using fast iterative shrinkage-thresholding algorithm with firm-thresholding: Acta Geophysica, 64, 1064–1092, doi: 10.1515/acgeo-2016-0043.
    Web of ScienceGoogle Scholar
  • Shan, H., J. Ma, and H. Yang, 2009, Comparisons of wavelets, contourlets and curvelets in seismic denoising: Journal of Applied Geophysics, 69, 103–115, doi: 10.1016/j.jappgeo.2009.08.002.JAGPEA0926-9851
    Web of ScienceGoogle Scholar
  • Trad, D., T. Ulrych, and M. Sacchi, 2003, Latest views of the sparse Radon transform: Geophysics, 68, 386–399, doi: 10.1190/1.1543224.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Trickett, S., 2008, F-xy Cadzow noise suppression: 78th Annual International Meeting, SEG, Expanded Abstracts, 2586–2590.
    Google Scholar
  • Tropp, J. A., and A. C. Gilbert, 2007, Signal recovery from random measurements via orthogonal matching pursuit: IEEE Transactions on Information Theory, 53, 4655–4666, doi: 10.1109/TIT.2007.909108.IETTAW0018-9448
    Web of ScienceGoogle Scholar
  • Wang, B., R.-S. Wu, X. Chen, and J. Li, 2015a, Simultaneous seismic data interpolation and denoising with a new adaptive method based on dreamlet transform: Geophysical Journal International, 201, 1180–1192.GJINEA0956-540X
    Web of ScienceGoogle Scholar
  • Wang, L., Y. Sun, and X. Cai, 2015b, Inpainting of historical seismograms using sparse representation method: Geophysical Journal International, 200, 679–691.GJINEA0956-540X
    Web of ScienceGoogle Scholar
  • Ye, M., Y. Qian, and J. Zhou, 2015, Multitask sparse nonnegative matrix factorization for joint spectral-spatial hyperspectral imagery denoising: IEEE Transactions on Geoscience and Remote Sensing, 53, 2621–2639, doi: 10.1109/TGRS.2014.2363101.IGRSD20196-2892
    Web of ScienceGoogle Scholar
  • Yu, S., J. Ma, X. Zhang, and M. D. Sacchi, 2015, Interpolation and denoising of high-dimensional seismic data by learning a tight frame: Geophysics, 80, no. 5, V119–V132, doi: 10.1190/geo2014-0396.1.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Zhang, C., Y. Li, H. Lin, and B. Yang, 2015, Signal preserving and seismic random noise attenuation by Hurst exponent based time-frequency peak filtering: Geophysical Journal International, 203, 901–909, doi: 10.1093/gji/ggv340.GJINEA0956-540X
    Web of ScienceGoogle Scholar
  • Zhang, R., and T. J. Ulrych, 2003, Physical wavelet frame denoising: Geophysics, 68, 225–231, doi: 10.1190/1.1543209.GPYSA70016-8033
    Web of ScienceGoogle Scholar
  • Zhao, X., Y. Li, G. Zhuang, C. Zhang, and X. Han, 2016, 2-D TFPF based on Contourlet transform for seismic random noise attenuation: Journal of Applied Geophysics, 129, 158–166, doi: 10.1016/j.jappgeo.2016.03.030.JAGPEA0926-9851
    Web of ScienceGoogle Scholar
  • Zhou, M., H. Chen, J. Paisley, L. Ren, L. Li, Z. Xing, D. Dunson, G. Sapiro, and L. Carin, 2012, Nonparametric Bayesian dictionary learning for analysis of noisy and incomplete images: IEEE Transactions on Image Processing, 21, 130–144, doi: 10.1109/TIP.2011.2160072.IIPRE41057-7149
    Web of ScienceGoogle Scholar
  • Zhou, Y., J. Gao, W. Chen, and P. Frossard, 2016, Seismic simultaneous source separation via patchwise sparse representation: IEEE Transactions on Geoscience and Remote Sensing, 54, 5271–5284, doi: 10.1109/TGRS.2016.2559514.IGRSD20196-2892
    Web of ScienceGoogle Scholar
  • Zu, S., H. Zhou, Y. Chen, S. Qu, X. Zou, H. Chen, and R. Liu, 2016, A periodically varying code for improving deblending of simultaneous sources in marine acquisition: Geophysics, 81, no. 3, V213–V225, doi: 10.1190/geo2015-0447.1.GPYSA70016-8033
    Web of ScienceGoogle Scholar