Sparsity- and continuity-promoting seismic image recovery with curvelet frames

Applied and Computational Harmonic Analysis

Volumn 24, Issue 2, 2008, Pages 150-173

  Herrmann, Felix J ^a   Moghaddam, Peyman ^a   Stolk, Christiaan C ^b  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC NOISE; APPROXIMATION THEORY; ASYMPTOTIC ANALYSIS; DATA STRUCTURES; IMAGE RECONSTRUCTION; NONLINEAR SYSTEMS; OPTIMIZATION; PROBLEM SOLVING;

CURVELET FRAMES; FRAME EXPANSION; IMAGE RECOVERY; MIGRATION AMPLITUDES; NONLINEAR OPTIMIZATION;

SEISMOGRAPHS;

EID: 38949176993     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2007.06.007     Document Type: Article

References (49)

1. Aminzadeh F., Brac J., and Kunz T. 3-D Salt and Overthrust Model. SEG/EAGE 3-D Modeling Series 1 (1997), SEG, Tulsa
2. Beylkin G. The inversion problem and applications of the generalized Radon transform. Comm. Pure Appl. Math. 37 (1984) 579-599
3. Black M.J., Sapiro G., and Marimont D. Robust anisotropic diffusion. IEEE Trans. Signal Process. 7 3 (1998) 421-432
4. Bleistein N., Cohen J., and Stockwell J. Mathematics of Multidimensional Seismic Imaging. Migration and Inversion (2001), Springer
5. Brandsberg-Dahl S., and de Hoop M.V. Focusing in DIP and AVA compensation on scattering-angle/azimuth common image gathers. Geophysics 68 1 (2003) 232-254
6. Candès E.J., and Donoho D.L. Continuous curvelet transform I: Resolution of the wavefront set. Appl. Comput. Harmon. Anal. 19 (2005) 162-197
7. Candès E.J., Demanet L., Donoho D.L., and Ying L. Fast discrete curvelet transforms. SIAM Multiscale Model. Simul. 5 3 (2006) 861-899
8. Candès E.J., and Donoho D.L. Continuous curvelet transform II: Discretization and frames. Appl. Comput. Harmon. Anal. 19 (2005) 198-222
9. Candès E.J., and Donoho D.L. Curvelets-A surprisingly effective nonadaptive representation for objects with edges. In: Schumaker L.L., et al. (Ed). Curves and Surfaces (2000), Vanderbilt Univ. Press
10. Candès E.J., and Donoho D.L. Recovering edges in ill-posed problems: Optimality of curvelet frames. Ann. Statist. 30 (2000) 784
11. 2 singularities. Comm. Pure Appl. Math. 57 2 (2004) 219-266
12. Candès E.J., and Guo F. New multiscale transforms, minimum total variation synthesis: Applications to edge-preserving image reconstruction. Signal Process. (2002) 1519-1543
13. Candès E.J., Romberg J., and Tao T. Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure Appl. Math. 59 8 (2006) 1207-1223
14. Chavent G., and Plessix R. An optimal true-amplitude least-squares prestack depth-migration operator. Geophysics 64 2 (1999) 508-515
15. Chen S.S., Donoho D.L., and Saunders M.A. Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 43 1 (2001) 129-159
16. Claerbout J., and Muir F. Robust modeling with erratic data. Geophysics 38 05 (1973) 826-844
17. J. Claerbout, D. Nichols, Spectral preconditioning, technical report, Stanford Exploration Project, 1994
18. Daubechies I., Defrise M., and de Mol C. An iterative thresholding algorithm for linear inverse problems with a sparsity constraints. Comm. Pure Appl. Math. 57 11 (2005) 1413-1457
19. de Hoop M.V., and Bleistein N. Generalized radon transform inversions for reflectivity in anisotropic elastic media. Inverse Problems 13 3 (1997) 669-690
20. de Hoop M.V., and Brandsberg-Dahl S. Maslov asymptotic extension of generalized radon transform inversion in anisotropic elastic media: A least-squares approach. Inverse Problems 16 3 (2000) 519-562
21. Donoho D.L. Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition. Appl. Comput. Harmon. Anal. 2 (1995) 101-126
22. Donoho D.L., Elad M., and Temlyakov V. Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans. Inform. Theory 52 (2006) 6-18
23. Elad M., Starck J.L., Querre P., and Donoho D.L. Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA). Appl. Comput. Harmon. Anal. 19 (2005) 340-358
24. Fehmers G.C., and Höcker C.F. Fast structural interpretation with structure-oriented filtering. Geophysics 68 4 (2003) 1286-1293
25. Figueiredo M., and Nowak R. An EM algorithm for wavelet-based image restoration. IEEE Trans. Image Process. (2003)
26. Guitton A. Amplitude and kinematic corrections of migrated images for nonunitary imaging operators. Geophysics 69 4 (2004) 1017-1024
27. Hennenfent G., and Herrmann F.J. Seismic denoising with non-uniformly sampled curvelets. Comp. Sci. Eng. 8 3 (2006) 16-25
28. Herrmann F.J. Multifractional splines: Application to seismic imaging. In: Unser M., and Aldroubi A. (Eds). Wavelets: Applications in Signal and Image Processing X. Proc. SPIE vol. 5207 (2003), SPIE 240-258
29. Herrmann F.J., Boeniger U., and Verschuur D.J. Nonlinear primary-multiple separation with directional curvelet frames. Geophys. J. Int. 170 (2007) 781-799
30. Hu J., Schuster G.T., and Valasek P.A. Poststack migration deconvolution. Geophysics 66 3 (2001) 939-952
31. Kuhl H., and Sacchi M. Least-squares wave-equation migration for AVP/AVA inversion. Geophysics 68 1 (2003) 262
32. Lee N.Y., and Lucier B.J. Wavelet methods for inverting the Radon transform with noisy data. IEEE Trans. Image Process. 10 (2001) 79-94
33. Nemeth T., Wu C., and Schuster G.T. Least-squares migration of incomplete reflection data. Geophysics 64 1 (1999) 208-221
34. O'Brien M., and Gray S. Can we image beneath salt?. Leading Edge 15 1 (1997) 17-22
35. Paige C.C., and Saunders M.A. LSQR: An algorithm for sparse linear equations and sparse least squares. ACM TOMS 8 1 (1982) 43-71
36. Plessix R., and Mulder W. Frequency-domain finite difference amplitude-preserving migration. Geophys. J. Int. 157 (2004) 975-987
37. Rickett J.E. Illumination-based normalization for wave-equation depth migration. Geophysics 68 4 (2003) 1371-1379
38. Schertzer O. Scale-space methods and regularization for denosing and inverse problems. Adv. Imag. Electron Phys. 128 (2003) 445-530
39. Starck J.L., Elad M., and Donoho D.L. Redundant multiscale transforms and their application to morphological component separation. Adv. Imag. Electron Phys. 132 (2004)
40. Stolk C.C. Microlocal analysis of a seismic linearized inverse problem. Wave Motion 32 (2000) 267-290
41. Stolk C.C., and Symes W.W. Smooth objective functionals for seismic velocity inversion. Inverse Problems 19 1 (2003) 73-89
42. W.W. Symes, Optimal scaling for reverse time migration, Geophysics, in press
43. Symes W.W. Reverse time migration with optimal checkpointing. Geophysics 72 5 (2007) SM213-SM221
44. Symes W.W., and Carazzone J. Velocity inversion by differential semblance optimization. Geophysics 56 (1991) 2061-2073
45. ten Kroode A.P.E., Smit D.-J., and Verdel A.R. A microlocal analysis of migration. Wave Motion 28 2 (1998) 149-172
46. Tibshirani R. Regression shrinkage and selection via the LASSO. J. Roy. Statist. Soc. B 58 1 (1997) 267-288
47. Tropp J.A. Just relax: Convex programming methods for identifying sparse signals in noise. IEEE Trans. Inform. Theory 52 3 (2006) 1030-1051
48. Tsaig Y., and Donoho D.L. Extensions of compressed sensing. Signal Process. 86 3 (2006) 549-571
49. Ying L., Demanet L., and Candés E.J. 3D Discrete Curvelet Transform. Proc. SPIE vol. 5914 (2005), SPIE p. 591413