Abstract：
In this paper, we explore the use of iterative curvelet thresholding for seismic random noise attenuation. A new method for combining the curvelet transform with iterative thresholding to suppress random noise is demonstrated and the issue is described as a linear inverse optimal problem using the L1 norm. Random noise suppression in seismic data is transformed into an L1 norm optimization problem based on the curvelet sparsity transform. Compared to the conventional methods such as median filter algorithm, FX deconvolution, and wavelet thresholding, the results of synthetic and field data processing show that the iterative curvelet thresholding proposed in this paper can sufficiently improve signal to noise radio (SNR) and give higher signal fidelity at the same time. Furthermore, to make better use of the curvelet transform such as multiple scales and multiple directions, we control the curvelet direction of the result after iterative curvelet thresholding to further improve the SNR.
WANG De-Li,TONG Zhong-Fei,TANG Chen et al. An iterative curvelet thresholding algorithm for seismic random noise attenuation[J]. APPLIED GEOPHYSICS, 2010, 7(4): 315-324.
[1]
Candès, E., and Donoho, D., 1999, Curvelets: A surprisingly effective non-adaptive representation of objects with edges, TN: Vanderbilt University Press, USA.
[2]
Candès, E., and Demanet, L., 2002, Curvelets and Fourier integral operators: Compte Rendus del’ Academie des Sciences, Paris, Serie I, 336, 395 - 398.
[3]
Candès, E., and Guo, F., 2002, New multiscale transforms, minimum total variation synthesis: Applications to edge-preserving image reconstruction: Signal Processing, 82, 1519 - 1543.
[4]
Candes, E., and Donoho, D., 2004, New tight frames of curvelets and optimal representations of objects with C2 singularities: Comm. Pure Appl. Math., 57(2), 219 - 266.
[5]
Candès, E., Demanet, L., and Donoho, D., 2006, Fast discrete curvelet transforms: SI-AM Multiscale Modeling and Simulation, 5, 861 - 899.
[6]
Daubechies, I., Defrise, M., and De Mol, C., 2004, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint: Comm. Pure and Appl. Math., 57, 1413 - 1457.
[7]
Elad, M., Starck, J. L., and Querre, P., 2005, Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA): Appl. Comput. Harmon. Anal, 19, 340 - 358.
[8]
Hennenfent, G., and Herrmann, F. J., 2004, Three-term amplitude-versus-offset (AVO) inversion revisited by curvelet and wavelet transforms: 74th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 211 - 214.
[9]
Hennenfent, G., and Herrmann, F. J., 2008, Simply denoise: Wavefield reconstruction via jittered undersampling: Geophysics, 73(3), V19 - V28.
[10]
Hennenfent, G., van den Berg, E., Friedlander, M. P., and Herrmann, F. J., 2008, New insights into one-norm solvers from the Pareto curve: Geophysics, 73(4), 23 - 26.
[11]
Herrmann, F. J., and Verschuur, E., 2004, Curvelet-domain multiple elimination with sparseness constraints: 74th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1333 - 1336.
[12]
Herrmann, F. J., Wang, D. L., and Hennenfent, G., 2007, Seismic data processing with curvelets: A multiscale and nonlinear approach: 77th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 2220 - 2224.
[13]
Herrmann, F. J., and Hennenfent, G., 2008, Non-parametric seismic data recovery with curvelet frames: Geophysical Journal International, 173(1), 233 - 248.
[14]
Huang, W., 2007, Research on curvelet transform and its applications on image processing: Masters Thesis, Xian University of Technology.
[15]
Huub, D., and Maarten, V., 2004, Wave-character preserving pre-stack map migration using curvelets: 74th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 961 - 964.
[16]
Neelamani, R., Baumstein, A. I., Gillard, D. G., and Hadidi, M. T., and Soroka, W. L., 2008, Coherent and random noise attenuation using the curvelet transform: The Leading Edge, 27(2), 240 - 248.
[17]
Wang, D. L., Saab, R., Yilmaz, ?., and Herrmann, F. J., 2008, Bayesian wavefield separation by transform-domain sparsity promotion: Geophysics, 73(5), A33 - A38.
[18]
Wang, W., Gao, J. H., Li, K., Ma, K., and Zhang, X., 2009, Structure-oriented Gaussian filter for seismic detail preserving smoothing: Image processing: 16th IEEE International Conference, 601 - 604.
[19]
Wu, F. P., 2008, Study on curvelet transform and its application in image processing: Masters Thesis, Jinan University.
[20]
Zhang, H. L., Zhang, Y. C., and Song, S., 2008, Curvelet domain-based prestack seismic data denoise method: Oil Geophysical Prospecting, l43(5), 508 - 513.
[21]
Zhao, X., 2007, Research and application of image denoising method based on curvelet transform: Masters Thesis, Shandong University of Science and Technology.
2010, Vol. 7 
