Seismic random noise attenuation using directional total variation in the shearlet domain
Kong, D., Peng, Z., Fan, H. and He, Y., 2016. Seismic random noise attenuation using directional total variation in the shearlet domain. Journal of Seismic Exploration, 25: 321-338. In this paper we propose an effective seismic denoising method using directional total variation (DTV) in the shearlet domain. This approach exploits the sparseness of shearlet transform and direction sensitivity of DTV. Shearlet shrinkage has a positive effect on denoising, but suffers from Gibbs artifact which can be solved by total variation (TV). DTV is an improved method of TV using anisotropic projection and performs well for the noisy signal with a dominant direction. The seismic data can be decomposed into several subbands by shearlet transform. Every subband has its own dominant direction. Therefore applying the direction information to DTV can more effectively eliminate seismic noise. The application on synthetic data and field data shows that the proposed method is superior to shearlet transform or DTV in seismogram noise removal and feature preservation.
- Alemie, W. and Sacchi, M.D., 2011. High-resolution three-term AVO inversion by means of a
- Trivariate Cauchy probability distribution. Geophysics, 76(3): R43-R55.
- Bayram, I. and Kamasak, M.E., 2012. Directional total variation. IEEE Sign. Process. Lett., 19:
- 781-784.
- Benning, M., Brune, C., Burger, M. and Miiller, J. 2013. Higher-order TV methods-enhancement
- via Bregman iteration. J. Scientif. Comput., 54: 269-310.
- Bredies, K., Kunisch, K. and Pock, T., 2010. Total generalized variation. SIAM J. Imag. Sci., 3:
- 492-526.
- Canales, L.L., 1984. Random noise reduction. Expanded Abstr., 54th Ann. Internat. SEG Mtg.,
- Atlanta.
- Do, M.N. and Vetterli, M., 2005,.The contourlet transform: An efficient directional multiresolution
- image representation. IEEE Transact. Image Process., 14: 2091-2106.
- Easley, G.R., Labate, D. and Lim, W., 2008. Sparse directional image representations using the
- discrete shearlet transform. Appl. Computat. Harmon. Analys., 25: 25-46.
- Easley, G.R., Labate, D. and Colonna, F., 2009. Shearlet-based total variation diffusion for
- denoising. IEEE Transact. Image Process., 18: 260-268.
- Figueiredo, M., Bioucas-Dias, J. and Nowak, R., 2007. Majorization-minimization algorithms for
- wavelet-based image restoration. IEEE Transact. Image Process., 16: 2980-2991.
- Guo, K. and Labate, D, 2007. Optimally sparse multidimensional representation using shearlets:
- SIAM J. Mathemat. Analys., 39: 298-318.
- Guo, W., Qin, J. and Yin, W., 2014. A new detail-preserving regularization scheme. SIAM J.
- Imag. Sci., 7: 1309-1334.
- Haghshenas Lari, H. and Gholami, A., 2014. Curvelet-TV regularized Bregman iteration for seismic
- random noise attenuation. J. Appl. Geophys., 109: 233-241.
- Hauser, S. and Steidl, G., 2013. Convex multiclass segmentation with shearlet regularization.
- Internat. J. Comput. Mathemat., 90: 62-81.
- Puryear, C.J. and Castagna, J.P., 2008. Layer-thickness determination and stratigraphic
- interpretation using spectral inversion: Theory and application. Geophysics, 73(2): R37-R48.
- Rudin, L.I., Osher, S. and Fatemi, E., 1992. Nonlinear total variation based noise removal
- algorithms. Physica D: Nonlinear Phenomena, 60: 259-268.
- 338 KONG, PENG, FAN & HE
- Shan, H., Ma, J. and Yang, H., 2009. Comparisons of wavelets, contourlets and curvelets in
- seismic denoising. J. Appl. Geophys., 69: 103-115.
- Starck, J.-L., Candés, E.J. and Donoho, D.L., 2002. The curvelet transform for image denoising.
- IEEE Transact. Image Process., 11: 670-684.
- Tang, G. and Ma, J., 2011. Application of total-variation-based curvelet shrinkage for
- three-dimensional seismic data denoising. IEEE Geosci. Remote Sens. Lett., 8: 103-107.
- Yi, S., Labate, D., Easley, G.R. and Krim, H., 2009. A shearlet approach to edge analysis and
- detection: IEEE Transactions on Image Processing. 18 (5), 929-941.
- Yilmaz, O., 2001. Seismic Data Analysis: Processing, Inversion, and Interpretation of Seismic Data.
- SEG, Tulsa, OK.
- Zhong, T., Li, Y., Wu, N., Nie, P. and Yang, B., 2015. Statistical properties of the random noise
- in seismic data. J. Appl. Geophys., 118: 84-91.
