Nonequispaced curvelet transform for seismic data reconstruction: A sparsity-promoting approach

Geophysics

Volumn 75, Issue 6, 2010, Pages

  Hennenfent, Gilles ^a,c   Fenelon, Lloyd ^b,d   Herrmann, Felix J ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b Laboratoire des Systèmes Photoniques   (France)

^c CHEVRON ENERGY TECHNOLOGY COMPANY   (United States)

^d BRITISH COLUMBIA CANCER RESEARCH CENTRE   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

FAST FOURIER TRANSFORMS; FOURIER ANALYSIS; INTERPOLATION; SEISMIC RESPONSE; SEISMIC WAVES;

CURVELET COEFFICIENTS; CURVELET TRANSFORMS; FAST DISCRETE CURVELET TRANSFORM (FDCT); FAST DISCRETE CURVELET TRANSFORMS; FOURIER COEFFICIENTS; RECONSTRUCTION ERROR; SECOND GENERATION; SEISMIC DATA RECONSTRUCTION;

GEOPHYSICAL PROSPECTING;

ACCURACY ASSESSMENT; DATA PROCESSING; DISCRETE ELEMENT METHOD; FOURIER TRANSFORM; INTERPOLATION; SEISMIC DATA; SEISMIC METHOD;

EID: 84857240428     PISSN: 00168033     EISSN: None     Source Type: Journal    
DOI: 10.1190/1.3494032     Document Type: Article

References (38)

1. Berkhout, A. J., and D. J. Verschuur, 1997, Estimation of multiple scattering by iterative inversion, part I: Theoretical considerations: Geophysics, 62, 1586-1595. gpy GPYSA7 0016-8033 10.1190/1.1444261
2. Candès, E. J., 1998, Ridgelets: Theory and applications: Ph.D. thesis, Stanford University.
3. Candès, E. J., L. Demanet, D. L. Donoho, and L. Ying, 2006, Fast discrete curvelet transforms: Multiscale Modeling and Simulation, 5, no. 3, 861-899. baf MMSUBT 1540-3459 10.1137/05064182X
4. Candès, E. J., and D. L. Donoho, 2000, Curvelets: A surprisingly effective nonadaptive representation of objects with edges, in Curve and surface fitting: Vanderbilt University Press, 105-120.
5. 1992, Earth soundings analysis: Processing versus inversion: Blackwell Scientific Publications.
6. 2 singularities: Communications on Pure and Applied Mathematics, 57, no. 2, 219-266. 10.1002/cpa.10116
7. Chen, S. S., D. L. Donoho, and M. A. Saunders, 1998, Atomic decomposition by basis pursuit: SIAM Journal on Scientific Computing, 20, no. 1, 33-61. 8sm SJOCE3 1064-8275 10.1137/S1064827596304010
8. Claerbout, J. F., 1971, Toward a unified theory of reflector mapping: Geophysics, 36, 467-481. gpy GPYSA7 0016-8033 10.1190/1.1440185
9. Córdoba, A., and C. Fefferman, 1978, Wave packets and Fourier integral operators: Communications in Partial Differential Equations, 3, no. 11, 979-1005. cpd CPDIDZ 0360-5302 10.1080/03605307808820083
10. Do, M. N., and M. Vetterli, 2002, Contourlets: A new directional multiresolution image representation: Proceedings of International Conference on Image Processing, IEEE, 1, 497-501.
11. Donoho, D. L., and M. R. Duncan, 1999, Digital curvelet transform: Strategy, implementation, and experiments: Technical report, Stanford Statistics Department.
12. Douma, H., and M. V. de Hoop, 2007, Leading-order seismic imaging using curvelets: Geophysics, 72, no. 6, S231-S248. gpy GPYSA7 0016-8033 10.1190/1.2785047
13. Feichtinger, H. G., and K. Grochenig, 1994, Theory and practice of irregular sampling, in Wavelets: Mathematics and applications: CRC Press, Studies in Advanced Mathematics 8, 305-363.
14. Guo, K., G. Kutyniok, and D. Labate, 2006, Sparse multidimensional representations using anisotropic dilation and shear operators, in G. Chen and M. J. Lai, eds., Wavelets and Splines: Nashboro Press, 189-201.
15. Guo, K., and D. Labate, 2007, Optimally sparse multidimensional representation using shearlets: SIAM Journal of Mathematical Analysis, 39, no. 1, 298-318, sma SJMAAH 0036-1410 10.1137/060649781
16. Hampson, D., 1986, Inverse velocity stacking for multiple elimination: Journal of the Canadian Society of Exploration Geophysicists, 22, no. 1, 44-45.
17. Hennenfent, G., and F. J. Herrmann, 2006, Seismic denoising with non-uniformly sampled curvelets: Computing in Science & Engineering, 8, no. 3, 16-25. 99u CSENFA 1521-9615 10.1109/MCSE.2006.49
18. 2008, Simply denoise: Wavefield reconstruction via jittered undersampling: Geophysics, 73, no. 3, V19-V28. gpy GPYSA7 0016-8033 10.1190/1.2841038
19. Herrmann, F. J., 2010, Randomized sampling and sparsity: Getting more information from fewer samples: Geophysics, this issue.
20. Herrmann, F. J., and G. Hennenfent, 2008, Non-parametric seismic data recovery with curvelet frames: Geophysical Journal International, 173, no. 1, 233-248. gji GJINEA 0956-540X 10.1111/j.1365-246X.2007.03698.x
21. Hindriks, K., and A. J. W. Duijndam, 2000, Reconstruction of 3-D seismic signals irregularly sampled along two spatial coordinates: Geophysics, 65, 253-263. gpy GPYSA7 0016-8033 10.1190/1.1444716
22. Kunis, S., 2006, Nonequispaced FFT: Generalisation and inversion: Ph.D. thesis, Lübeck University.
23. Lu, Y. M., and M. N. Do, 2007, Multidimensional directional filter banks and surfacelets: IEEE Transactions on Image Processing, 16, no. 4, 918-931. iei IIPRE4 1057-7149 10.1109/TIP.2007.891785
24. Mallat, S., 1999, A wavelet tour of signal processing, second edition: Academic Press.
25. Potts, D., G. Steidl, and M. Tasche, 2001, Fast Fourier transforms for nonequispaced data: A tutorial, in J. J. Benedetto, and P. Ferreira, eds., Modern sampling theory: Mathematics and applications: Birkhauser, 12, 249-274.
26. Sacchi, M. D., T. J. Ulrych, and C. J. Walker, 1998, Interpolation and extrapolation using a high-resolution discrete Fourier transform: IEEE Transactions on Signal Processing, 46, no. 1, 31-38. itl ITPRED 1053-587X 10.1109/78.651165
27. Schonewille, M. A., 2000, Fourier reconstruction of irregularly sampled seismic data: Ph.D. thesis, Delft University of Technology.
28. Smith, H., 1998, A hardy space for Fourier integral operators: Journal of Geometric Analysis, 8, no. 4, 629-653. b7p JGANEG 1050-6926
29. Snieder, R., 1993, Global inversions using normal mode and long-period surface waves: Chapman and Hall.
30. Spitz, S., 1991, Seismic trace interpolation in the FX domain: Geophysics, 56, 785-794. gpy GPYSA7 0016-8033 10.1190/1.1443096
31. Starck, J.-L., E. J. Candès, and D. L. Donoho, 2002, The curvelet transform for image denoising: IEEE Transactions on Image Processing, 11, no. 6, 670-684. iei IIPRE4 1057-7149 10.1109/TIP.2002.1014998
32. Symes, W. W., 2007, Reverse time migration with optimal checkpointing: Geophysics, 72, no. 5, SM213-SM221. gpy GPYSA7 0016-8033 10.1190/1.2742686
33. Tang, G., R. Shahidi, J. Ma, and F. J. Herrmann, 2009, Design of two-dimensional randomized sampling schemes for curvelet-based sparsity-promoting seismic data recovery: Technical Report TR-2009-03, Earth and Ocean Sciences Department, The University of British Columbia.
34. Thorson, J. R., and J. F. Claerbout, 1985, Velocity-stack and slant-stack stochastic inversion: Geophysics, 50, 2727-2741. gpy GPYSA7 0016-8033 10.1190/1.1441893
35. Trad, D., T. J. Ulrych, and M. D. Sacchi, 2003, Latest views of the sparse Radon transform: Geophysics, 68, 386-399. gpy GPYSA7 0016-8033 10.1190/1.1543224
36. Verschuur, D. J., and A. J. Berkhout, 1997, Estimation of multiple scattering by iterative inversion, part II: Practical aspects and examples: Geophysics, 62, 1596-1611. gpy GPYSA7 0016-8033 10.1190/1.1444262
37. Ying, L., L. Demanet, and E. J. Candès, 2005, 3-D discrete curvelet transform: Proceedings of Wavelets XI, SPIE, 5914, 344-354.
38. Zwartjes, P. M., 2005, Fourier reconstruction with sparse inversion: Ph.D. thesis, Delft University of Technology.