Discrete almost-symmetric wave packets and multiscale geometrical representation of (Seismic) waves

IEEE Transactions on Geoscience and Remote Sensing

Volumn 48, Issue 9, 2010, Pages 3408-3423

  Duchkov, Anton A ^a   Andersson, Fredrik ^b,c,d   De Hoop, Maarten V ^d  

^a TROFIMUK INSTITUTE OF PETROLEUM GEOLOGY AND GEOPHYSICS   (Russian Federation)

^b LUND UNIVERSITY   (Sweden)

^c Center for Computational and Applied Mathematics   (United States)

^d PURDUE UNIVERSITY   (United States)

Author keywords

Dyadic parabolic decomposition; Seismology; Wave packets

Indexed keywords

ADJOINTS; DE-NOISING; DIRECTIONAL REGULARITY; DISCRETE TRANSFORMS; DISCRETIZATION SCHEME; DYADIC PARABOLIC DECOMPOSITION; GEOMETRICAL REPRESENTATION; HIGHER-DIMENSIONAL; MULTISCALES; PARABOLIC SCALING; PHASE SPACES; PLANE WAVE; UNEQUALLY SPACED FAST FOURIER TRANSFORM;

FAST FOURIER TRANSFORMS; FEATURE EXTRACTION; PHASE SPACE METHODS; SEISMOLOGY; WAVES;

WAVE PACKETS;

DATA SET; DISCRETE CHOICE ANALYSIS; FOURIER TRANSFORM; GEOMETRY; PARAMETERIZATION; SEISMIC WAVE; SEISMOLOGY; THREE-DIMENSIONAL MODELING;

EID: 77956060495     PISSN: 01962892     EISSN: None     Source Type: Journal    
DOI: 10.1109/TGRS.2010.2046177     Document Type: Article

References (46)

1. M. Grasmueck and D. Viggiano, "Integration of ground-penetrating radar and laser position sensors for real-time 3-D data fusion," IEEE Trans. Geosci. Remote Sens., vol.45, no.1, pp. 130-137, Jan. 2007.
2. T. Counts, A. Gurbuz, W. Scott, Jr., J. McClellan, and K. Kim, "Multistatic ground-penetrating radar experiments," IEEE Trans. Geosci. Remote Sens., vol.45, no.8, pp. 2544-2553, Aug. 2007.
3. K. Belli, C. Rappaport, H. Zhan, and S. Wadia-Fascetti, "Effectiveness of 2-D and 2.5-D FDTD ground-penetrating radar modeling for bridgedeck deterioration evaluated by 3-D FDTD," IEEE Trans. Geosci. Remote Sens., vol.47, no.11, pp. 3656-3663, Nov. 2009.
4. J.-G. Zhao and M. Sato, "Radar polarimetry analysis applied to singlehole fully polarimetric borehole radar," IEEE Trans. Geosci. Remote Sens., vol.44, no.12, pp. 3547-3554, Dec. 2006.
5. S. Kidera, T. Sakamoto, and T. Sato, "High-resolution and real-time three-dimensional imaging algorithm with envelopes of spheres for UWB radars," IEEE Trans. Geosci. Remote Sens., vol.46, no.11, pp. 3503- 3513, Nov. 2008.
6. F. Ahmad, Y. Zhang, and M. Amin, "Three-dimensional wideband beamforming for imaging through a single wall," IEEE Geosci. Remote Sens. Lett., vol.5, no.2, pp. 176-179, Apr. 2008.
7. F. Lombardini, "Differential tomography: A new framework for SAR interferometry," IEEE Trans. Geosci. Remote Sens., vol.43, no.1, pp. 37- 44, Jan. 2005.
8. S. Jun, Z. Xiaoling, J. Yang, and W. Yinbo, "Surface-tracing-based LASAR 3-D imaging method via multiresolution approximation," IEEE Trans. Geosci. Remote Sens., vol.46, no.11, pp. 3719-3730, Nov. 2008.
9. N. Plant, K. Holland, andM. Haller, "Ocean wave number estimation from wave-resolving time-series imagery," IEEE Trans. Geosci. Remote Sens., vol.46, no.9, pp. 2644-2658, Sep. 2008.
10. A. Mandal, S. Pal, A. De, and S. Mitra, "Novel approach to identifying good tracer clouds from a sequence of satellite images," IEEE Trans. Geosci. Remote Sens., vol.43, no.4, pp. 813-818, Apr. 2005.
11. P. Héas and E. Mémin, "Three-dimensional motion estimation of atmospheric layers from image sequences," IEEE Trans. Geosci. Remote Sens., vol.46, no.8, pp. 2385-2396, Aug. 2008.
12. I. Daubechies, "The wavelet transform, time-frequency localization and signal analysis," IEEE Trans. Inf. Theory, vol.36, no.5, pp. 961-1005, Sep. 1990.
13. A. Roy, C.-H. Wen, J. Doherty, and J. Mathews, "Signal feature extraction from microbarograph observations using the Hilbert-Huang transform," IEEE Trans. Geosci. Remote Sens., vol.46, no.5, pp. 1442-1447, May 2008.
14. V. Chandrasekaran, M. Wakin, D. Baron, and R. Baraniuk, "Representation and compression of multidimensional piecewise functions using surflets," IEEE Trans. Inf. Theory, vol.55, no.1, pp. 347-400, Jan. 2009.
15. E. Simoncelli and W. Freeman, "The steerable pyramide: A flexible architechture for multiscale derivate computation," in Proc. IEEE Conf. Imag., 1995, vol.3, pp. 444-447.
16. F. Meyer and R. Coifman, "Brushlets: A tool for directional image analysis and image compression," Appl. Comput. Harmon. Anal., vol.4, no.2, pp. 147-187, Apr. 1997.
17. E. Candès and D. Donoho, "New tight frames of curvelets and optimal representations of objects with piecewise-C2 singularities," Commun. Pure Appl. Math., vol.57, no.2, pp. 219-266, 2004.
18. D. Labate, W.-Q. Lim, G. Kutyniok, and G. Weiss, "Sparse multidimensional representation using shearlets," Proc. SPIE, vol.5914, pp. 254- 262, 2005.
19. H. Smith, "A parametrix construction for wave equations with C1,1 coefficients," Ann. Inst. Fourier, Grenoble, vol.48, no.3, pp. 797-835, 1998.
20. F. Andersson, M. De Hoop, H. Smith, and G. Uhlmann, "A multiscale approach to hyperbolic evolution equations with limited smoothness," Commun. Partial Differential Equations, vol.33, no.6, pp. 988-1017, Jun. 2008.
21. T. Stöcker, "Weyl filters for linear array data," IEEE Trans. Geosci. Remote Sens., vol.41, no.3, pp. 697-707, Mar. 2003.
22. E. Stein, Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton, NJ: Princeton Univ. Press, 1993.
23. E. Candès and D. Donoho, "Continuous curvelet transform I: Resolution of the wavefront set," Appl. Comput. Harmon. Anal., vol.19, no.2, pp. 162-197, Sep. 2005.
24. E. Candès and D. Donoho, "Continuous curvelet transform II: Discretization and frames," Appl. Comput. Harmon. Anal., vol.19, no.2, pp. 198- 222, Sep. 2005.
25. E. Candès, L. Demanet, D. Donoho, and L. Ying, "Fast discrete curvelet transforms," SIAM Multiscale Model. Simul., vol.5, no.3, pp. 861-899, Sep. 2006.
26. A. Dutt and V. Rokhlin, "Fast Fourier transforms for nonequispaced data," SIAM J. Sci. Comput., vol.14, no.6, pp. 1368-1393, Nov. 1993.
27. G. Beylkin, "On the fast Fourier transform of functions with singularities," Appl. Comput. Harmon. Anal., vol.2, no.4, pp. 363-381, Oct. 1995.
28. I. Daubechies, M. Defrise, and C. De Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Commun. Pure Appl. Math., vol.57, no.11, pp. 1413-1457, Aug. 2004.
29. T. Rouphael and J. Cruz, "Multichannel trace interpolation in the presence of spatial aliasing," IEEE Trans. Geosci. Remote Sens., vol.36, no.3, pp. 1025-1030, May 1998.
30. S. Pop, O. Lavaille, M. Donias, R. Trebes, M. Borda, S. Guillon, and N. Keskes, "A PDE-based approach to three-dimensional seismic data fusion," IEEE Trans. Geosci. Remote Sens., vol.46, no.5, pp. 1385-1393, May 2008.
31. F. Herrmann, P. Moghaddam, and C. Stolk, "Sparsity- and continuitypromoting seismic image recovery with curvelet frames," Appl. Comput. Harmon. Anal., vol.24, no.2, pp. 150-173, Mar. 2008.
32. F. de Melo, G. Borges, and J. Soares, "Automatic wave group identification on deep seismic refraction data using SMF clustering," IEEE Geosci. Remote Sens. Lett., vol.5, no.4, pp. 687-690, Oct. 2008.
33. D. Gibson, M. Spann, J. Turner, and T. Wright, "Fault surface detection in 3-D seismic data," IEEE Trans. Geosci. Remote Sens., vol.43, no.9, pp. 2094-2102, Sep. 2005.
34. F. Soldovieri, A. Brancaccio, G. Prisco, G. Leone, and R. Pierri, "Kirchhoff-based shape reconstruction algorithm for the multimonostatic configuration: The realistic case of buried pipes," IEEE Trans. Geosci. Remote Sens., vol.46, no.10, pp. 1031-3038, Oct. 2008.
35. J. Song, Q. Liu, P. Torrione, and L. Collins, "Two-dimensional and three-dimensional NUFFT migrationmethod for landmine detection using ground-penetrating radar," IEEE Trans. Geosci. Remote Sens., vol.44, no.6, pp. 1462-1469, Jun. 2006.
36. H. Douma and M. De Hoop, "Leading-order seismic imaging using curvelets," Geophysics, vol.72, no.6, pp. S231-S248, Oct. 2007.
37. M. De Hoop, H. Smith, G. Uhlmann, and R. Van der Hilst, "Seismic imaging with the generalized Radon transform: A curvelet transform perspective," Inv. Probl., vol.25, no.2, p. 025 005, Feb. 2008, DOI:10.1088/0266-5611/25/2/025 005.
38. V. Brytik, M. De Hoop, and M. Salo, "Sensitivity analysis of waveequation tomography: A multiscale approach," J. Fourier Anal. Appl., 2010, to be published.
39. H. Smith, "A hardy space for Fourier integral operators," J. Geom. Anal., vol.8, no.4, pp. 629-654, Jul. 1998.
40. C. Ronchi, R. Ianoco, and P. Paolucci, "The 'cubed sphere': A new method for the solution of partial differential equations in spherical geometry," J. Comput. Phys., vol.124, no.1, pp. 93-114, Mar. 1996.
41. O. Yilmaz, Seismic Data Analysis: Processing, Inversion, and Interpretation of Seismic Data. Tulsa, OK: Soc. Explor. Geophys., 2001.
42. X. Feng, M. Sato, C. Liu, and Y. Zhang, "Profiling and rough surface by migration," IEEE Geosci. Remote Sens. Lett., vol.6, no.2, pp. 258-262, Apr. 2009.
43. B. Hua and G. A. McMechan, "Parsimonious 2-D prestack Kirchhoff depth migration," Geophysics, vol.68, no.3, pp. 1043-1051, 2003.
44. O. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation. Philadelphia, PA: SIAM, 2005.
45. J. Minet, S. Lambot, E. Slob, and M. Vanclooster, "Soil-surface water content estimation by full-waveform GPR signal inversion in the presence of thin layers," IEEE Trans. Geosci. Remote Sens., vol.48, no.3, pt. 1, pp. 1138-1150, Mar. 2010.
46. T. van Leeuwen and W. Mulder, "Velocity analysis based on data correlation," Geophys. Prospect., vol.56, no.6, pp. 791-803, Nov. 2008.