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Volume 68, Issue 3
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Tensor algebra provides a robust framework for multi‐dimensional seismic data processing. A low‐rank tensor can represent a noise‐free seismic data volume. Additive random noise will increase the rank of the tensor. Hence, tensor rank‐reduction techniques can be used to filter random noise. Our filtering method adopts the Candecomp/Parafac decomposition to approximates a ‐dimensional seismic data volume via the superposition of rank‐one tensors. Similar to the singular value decomposition for matrices, a low‐rank Candecomp/Parafac decomposition can capture the signal and exclude random noise in situations where a low‐rank tensor can represent the ideal noise‐free seismic volume. The alternating least squares method is adopted to compute the Candecomp/Parafac decomposition with a provided target rank. This method involves solving a series of highly over‐determined linear least‐squares subproblems. To improve the efficiency of the alternating least squares algorithm, we uniformly randomly sample equations of the linear least‐squares subproblems to reduce the size of the problem significantly. The computational overhead is further reduced by avoiding unfolding and folding large dense tensors. We investigate the applicability of the randomized Candecomp/Parafac decomposition for incoherent noise attenuation via experiments conducted on a synthetic dataset and field data seismic volumes. We also compare the proposed algorithm (randomized Candecomp/Parafac decomposition) against multi‐dimensional singular spectrum analysis and classical prediction filtering. We conclude the proposed approach can achieve slightly better denoising performance in terms of signal‐to‐noise ratio enhancement than traditional methods, but with a less computational cost.

© 2020 European Association of Geoscientists & Engineers © 2019 European Association of Geoscientists & Engineers
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2019-11-20
2024-04-26

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References

  1. AbmaR. and ClaerboutJ.1995. Lateral prediction for noise attenuation by t‐x and f‐x techniques. Geophysics60, 1887–1896.
     [Google Scholar]
  2. AkaikeH.1969. Fitting autoregressive models for prediction. Annals of the Institute of Statistical Mathematics21, 243–247.
     [Google Scholar]
  3. BattaglinoC., BallardG. and KoldaT.G.2018. A practical randomized CP tensor decomposition. SIAM Journal on Matrix Analysis and Applications39, 876–901.
     [Google Scholar]
  4. BerkhoutA.2008. Changing the mindset in seismic data acquisition. The Leading Edge27, 924–938.
     [Google Scholar]
  5. CanalesL.L. 1984. Random noise reduction. 54th SEG Annual Meeting, Atlanta, GA, USA. Expanded Abstracts, 525–527.
  6. ChaseM.K.1992. Random noise reduction by FXY prediction filtering. Exploration Geophysics23, 51–55.
     [Google Scholar]
  7. ComonP., LucianiX. and De AlmeidaA.L.2009. Tensor decompositions, alternating least squares and other tales. Journal of Chemometrics23, 393–405.
     [Google Scholar]
  8. ElbothT., PresterudI.V. and HermansenD.2010. Time‐frequency seismic data de‐noising. Geophysical Prospecting58, 441–453.
     [Google Scholar]
  9. GaoJ., ChengJ. and SacchiM.D.2015. A new 5D seismic reconstruction method based on a parallel square matrix factorization algorithm. 85th SEG Annual Meeting, New Orleans, LA, USA. Expanded Abstracts, 3784–3788.
  10. GaoJ., SacchiM.D. and ChenX.2011. A fast rank reduction method for the reconstruction of 5D seismic volumes. 81st SEG Annual Meeting, San Antonio, TX, USA. Expanded Abstracts, 3622–3627.
  11. GülünayN.1986. FXDECON and complex Wiener prediction filter. 86th SEG Annual Meeting, Houston, TX, USA. Expanded Abstracts, 279–281.
  12. GülünayN.2000. Noncausal spatial prediction filtering for random noise reduction on 3‐D poststack data. Geophysics65, 1641–1653.
     [Google Scholar]
  13. HarshmanR.A.1970. Foundations of the PARAFAC procedure: models and conditions for an “explanatory” multi‐modal factor analysis. UCLA Workshop Papers in Phonetics 16.
  14. HerrmannF.J., WangD., HennenfentG. and MoghaddamP.P.2007. Curvelet‐based seismic data processing: a multiscale and nonlinear approach. Geophysics73, A1–A5.
     [Google Scholar]
  15. IbrahimA. and SacchiM.D.2013. Simultaneous source separation using a robust Radon transform. Geophysics79, V1–V11.
     [Google Scholar]
  16. KoldaT.G. and BaderB.W.2009. Tensor decompositions and applications. SIAM Review51, 455–500.
     [Google Scholar]
  17. KreimerN. and SacchiM.2011. Evaluation of a new 5D seismic volume reconstruction method: Tensor completion versus Fourier reconstruction. GeoConvention, Calgary, Canada.
  18. KreimerN. and SacchiM.D.2012. A tensor higher‐order singular value decomposition for prestack seismic data noise reduction and interpolation. Geophysics77, V113–V122.
     [Google Scholar]
  19. LiuB. and SacchiM.D.2004. Minimum weighted norm interpolation of seismic records. Geophysics69, 1560–1568.
     [Google Scholar]
  20. LubinM. and DunningI.2015. Computing in operations research using Julia. INFORMS Journal on Computing27, 238–248.
     [Google Scholar]
  21. OropezaV. and SacchiM.2011. Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis. Geophysics76(3), V25–V32.
     [Google Scholar]
  22. PhanA.‐H., TichavskỳP. and CichockiA.2013. Fast alternating LS algorithms for high order CANDECOMP/PARAFAC tensor factorizations. IEEE Transactions on Signal Processing61, 4834–4846.
     [Google Scholar]
  23. PhanA.‐H., TichavskỳP. and CichockiA.2015. Tensor deflation for CANDECOMP/PARAFAC ‐ Part II: Initialization and error analysis. IEEE Transactions on Signal Processing63, 5939–5950.
     [Google Scholar]
  24. RichardsonA. and FellerC.2019. Seismic data denoising and deblending using deep learning. arXiv preprint arXiv:1907.01497.
  25. RokhlinV. and TygertM.2008. A fast randomized algorithm for overdetermined linear least‐squares regression. Proceedings of the National Academy of Sciences105, 13212–13217.
     [Google Scholar]
  26. SacchiM.D., GaoJ., StantonA. and ChengJ.2015. Tensor factorization and its application to multidimensional seismic data recovery. 85th SEG Annual Meeting, New Orleans, LA, USA. Expanded Abstracts, 4827–4831.
  27. SacchiM.D. and KuehlH.2001. ARMA formulation of f‐x prediction error filters and projection filters. Journal of Seismic Exploration9, 185–198.
     [Google Scholar]
  28. SacchiM.D. and UlrychT.J.1995. High‐resolution velocity gathers and offset space reconstruction. Geophysics60, 1169–1177.
     [Google Scholar]
  29. SacchiM.D., UlrychT.J., and WalkerC.J.1998. Interpolation and extrapolation using a high‐resolution discrete Fourier transform. IEEE Transactions on Signal Processing46, 31–38.
     [Google Scholar]
  30. SidiropoulosN.D., De LathauwerL., FuX., HuangK., PapalexakisE.E. and FaloutsosC.2017. Tensor decomposition for signal processing and machine learning. IEEE Transactions on Signal Processing65, 3551–3582.
     [Google Scholar]
  31. SoubarasR.1994. Signal‐preserving random noise attenuation by the f‐x projection. 64th SEG Annual Meeting, Los Angeles, CA, USA. Expanded Abstracts, 1576–1579.
  32. SoubarasR.1995. Prestack random and impulsive noise attenuation by f‐x projection filtering. 65th SEG Annual Meeting, Houston, TX, USA. Expanded Abstracts, 711–714.
  33. StarckJ.‐L., CandèsE.J. and DonohoD.L.2002. The curvelet transform for image denoising. IEEE Transactions on Image Processing11, 670–684.
     [Google Scholar]
  34. TradD.O., UlrychT.J., SacchiM.D.2002. Accurate interpolation with high‐resolution time‐variant Radon transforms. Geophysics67, 644–656.
     [Google Scholar]
  35. TrickettS., BurroughsL., MiltonA., WaltonL. and DackR.2010. Rank‐reduction‐based trace interpolation. 80th SEG Annual Meeting, Denver, CO, USA. Expanded Abstracts, 3829–3833.
  36. TrickettS.R.2003. F‐xy eigenimage noise suppression. Geophysics68, 751–759.
     [Google Scholar]
  37. WangE., NealonJ.2019. Applying machine learning to 3D seismic image denoising and enhancement. Interpretation7(3), SE131–SE139.
     [Google Scholar]
  38. WangF. and ChenS.2019. Residual learning of deep convolutional neural network for seismic random noise attenuation. IEEE Geoscience and Remote Sensing Letters16, 1314–1318.
     [Google Scholar]
  39. WangJ., NgM. and PerzM.2010. Seismic data interpolation by greedy local Radon transform. Geophysics75, WB225–WB234.
     [Google Scholar]
  40. WangY., TungH.‐Y., SmolaA.J. and AnandkumarA.2015. Fast and guaranteed tensor decomposition via sketching. Advances in Neural Information Processing Systems28, 991–999.
     [Google Scholar]
  41. XuY., HaoR., YinW. and SuZ.2015. Parallel matrix factorization for low‐rank tensor completion. American Institute of Mathematical Sciences9, 601–624.
     [Google Scholar]
  42. ZhangK., ZuoW., ChenY., MengD. and ZhangL.2017. Beyond a Gaussian denoiser: residual learning of deep CNN for image denoising. IEEE Transactions on Image Processing26, 3142–3155.
     [Google Scholar]
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Random noise attenuation via the randomized canonical polyadic decomposition
Geophysical Prospecting 68, 872 (2020); https://doi.org/10.1111/1365-2478.12894
/content/journals/10.1111/1365-2478.12894
/content/journals/10.1111/1365-2478.12894
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  • Article Type: Research Article
Keyword(s): Multi‐linear algebra; Noise; Signal processing

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