Reconstruction of 3D non-uniformly sampled seismic data along two spatial coordinates using non-equispaced curvelet transform

References

• Candès, E. J., 1998, Ridgelets: theory and applications: Ph.D. thesis, Stanford University.
   Google Scholar
• Candès E. J. Donoho D. L. 2004 New tight frames of curvelets and optimal representations of objects with piecewise-C2 singularities: Communications on Pure and Applied Mathematics 57 219 266 10.1002/cpa.10116
   Web of Science ®Google Scholar
• Candès E. J. Demanet L. Donoho D. Ying L. 2006 Fast discrete curvelet transforms: SIAM Multiscale Modeling and Simulation 5 861 899 10.1137/05064182X
   Web of Science ®Google Scholar
• Cao J. J. Zhao J. T. 2016 Simultaneous seismic interpolation and denoising based on sparse inversion with a 3D low redundancy curvelet transform: Exploration Geophysics 47 213 220
   Google Scholar
• Cao J. J. Wang Y. F. Wang B. F. 2015 Accelerating seismic interpolation with a gradient projection method based on tight frame property of curvelet: Exploration Geophysics 46 253 260 10.1071/EG14016
   Web of Science ®Google Scholar
• Chen S. S. Donoho D. L. Saunders M. A. 1998 Atomic decomposition by basis pursuit: SIAM Journal on Scientific Computing 20 33 61 10.1137/S1064827596304010
   Web of Science ®Google Scholar
• Chiu S. K. 2014 Multidimensional interpolation using a model-constrained minimum weighted norm interpolation: Geophysics 79 V191 V199 10.1190/geo2014-0086.1
   Web of Science ®Google Scholar
• Duijndam A. J. W. Schonewille M. A. Hindriks C. O. H. 1999 Reconstruction of band-limited signals, irregularly sampled along one spatial direction: Geophysics 64 524 538 10.1190/1.1444559
   Web of Science ®Google Scholar
• Ely G. Aeron S. Ning H. Kilmer M. E. 2015 5D seismic data completion and denoising using a novel class of tensor decompositions: Geophysics 80 V83 V95 10.1190/geo2014-0467.1
   Web of Science ®Google Scholar
• Fomel S. 2003 Seismic reflection data interpolation with differential offset and shot continuation: Geophysics 68 733 744 10.1190/1.1567243
   Web of Science ®Google Scholar
• Fomel S. Liu Y. 2010 Seislet transform and seislet frame: Geophysics 75 V25 V38 10.1190/1.3380591
   Web of Science ®Google Scholar
• Gan S. Wang S. Chen Y. 2016 Compressive sensing for seismic data reconstruction via fast projection onto convex sets based on seislet transform: Journal of Applied Geophysics 130 194 208 10.1016/j.jappgeo.2016.03.033
   Web of Science ®Google Scholar
• Gao J. J. Stanton A. Sacchi M. D. 2015 Parallel matrix factorization algorithm and its application to 5D seismic reconstruction and denoising: Geophysics 80 V173 V187 10.1190/geo2014-0594.1
   Web of Science ®Google Scholar
• Hennenfent G. Herrmann F. J. 2008 Simply denoise: wavefield reconstruction via jittered undersampling: Geophysics 73 V19 V28 10.1190/1.2841038
   Web of Science ®Google Scholar
• Hennenfent G. Fenelon L. Herrmann F. J. 2010 Nonequispaced curvelet transform for seismic data reconstruction: a sparsity-promoting approach: Geophysics 75 WB203 WB210 10.1190/1.3494032
   Web of Science ®Google Scholar
• Herrmann F. J. 2010 Randomized sampling and sparsity: getting more information from fewer samples: Geophysics 75 WB173 WB187 10.1190/1.3506147
   Web of Science ®Google Scholar
• Herrmann F. J. Hennenfent G. 2008 Non-parametric seismic data recovery with curvelet frames: Geophysical Journal International 173 233 248 10.1111/j.1365-246X.2007.03698.x
   Web of Science ®Google Scholar
• Hindriks C. O. H. Duijndam A. J. W. 2000 Reconstruction of 3D seismic signals irregularly sampled along two spatial coordinates: Geophysics 65 253 263 10.1190/1.1444716
   Web of Science ®Google Scholar
• Jin S. 2010 5D seismic data regularization by a damped least-norm Fourier inversion: Geophysics 75 WB103 WB111 10.1190/1.3505002
   Web of Science ®Google Scholar
• Kim B. Jeong S. Byun J. 2016 An efficient interpolation approach for insufficient 3D field data: Exploration Geophysics 47 213 220
   Google Scholar
• Kreimer N. Stanton A. Sacchi M. D. 2013 Tensor completion based on nuclear norm minimization for 5D seismic data reconstruction: Geophysics 78 V273 V284 10.1190/geo2013-0022.1
   Web of Science ®Google Scholar
• Krilov D. Vaniarho Y. Basaev D. 2016 Smart averaging interpolation algorithm comparative test: Geophysical Prospecting 64 642 656 10.1111/1365-2478.12332
   Web of Science ®Google Scholar
• Kumar R. Silva C. Akalin O. Aravkin A. Mansour H. 2015 Efficient matrix completion for seismic data reconstruction: Geophysics 80 V97 V114 10.1190/geo2014-0369.1
   Web of Science ®Google Scholar
• Kunis, S., 2006, Nonequispaced FFT: generalisation and inversion: Ph.D. thesis, Lübeck University.
   Google Scholar
• Ma J. 2013 Three-dimensional irregular seismic data reconstruction via low-rank matrix completion: Geophysics 78 V181 V192 10.1190/geo2012-0465.1
   Web of Science ®Google Scholar
• Naghizadeh M. Sacchi M. D. 2007 Multistep autoregressive reconstruction of seismic records: Geophysics 72 V111 V118 10.1190/1.2771685
   Web of Science ®Google Scholar
• Naghizadeh M. Sacchi M. D. 2010 Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data: Geophysics 75 WB189 WB202 10.1190/1.3509468
   Web of Science ®Google Scholar
• Oropeza V. Sacchi M. D. 2011 Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis: Geophysics 76 V25 V32 10.1190/1.3552706
   Web of Science ®Google Scholar
• Ronen J. 1987 Wave equation trace interpolation: Geophysics 52 973 984 10.1190/1.1442366
   Web of Science ®Google Scholar
• Spitz S. 1991 Seismic trace interpolation in the f-x domain: Geophysics 56 785 794 10.1190/1.1443096
   Web of Science ®Google Scholar
• Trad D. 2009 Five-dimensional interpolation: recovering from acquisition constraints: Geophysics 74 V123 V132 10.1190/1.3245216
   Web of Science ®Google Scholar
• Turquais, P., Asgedom, E., and Soellner, W., 2017, Structured dictionary learning for interpolation of aliased seismic data: SEG Technical Program Expanded Abstracts, 4257–4261.
   Google Scholar
• van den Berg E. Friedlander M. P. 2009 Probing the Pareto frontier for basis pursuit solutions: SIAM Journal on Scientific Computing 31 890 912 10.1137/080714488
   Web of Science ®Google Scholar
• Whiteside, W., Guo, M., Sun, J., and Wang, B., 2014, 5D data regularization using enhanced antileakage Fourier transform: SEG Technical Program Expanded Abstracts, 3616–3620.
   Google Scholar
• Xu S. Zhang Y. Pham D. Lambaré G. 2005 Antileakage Fourier transform for seismic data regularization: Geophysics 70 V87 V95 10.1190/1.1993713
   Web of Science ®Google Scholar
• Xu S. Zhang Y. Pham D. Lambaré G. 2010 Antileakage Fourier transform for seismic data regularization in higher dimensions: Geophysics 75 WB113 WB120 10.1190/1.3507248
   Web of Science ®Google Scholar
• Xue Y. Ma J. Chen X. 2014 High-order sparse Radon transform for AVO-preserving data reconstruction: Geophysics 79 V13 V22 10.1190/geo2013-0002.1
   Web of Science ®Google Scholar
• Yang, H., Li, J., and Ma, S., 2015, A fast Fourier inversion strategy for 5D seismic data regularization: SEG Technical Program Expanded Abstracts, 3910–3914.
   Google Scholar
• Yu S. W. Ma J. W. Osher S. 2016 Monte Carlo data-driven tight frame for seismic data recovery: Geophysics 81 V327 V340 10.1190/geo2015-0343.1
   Web of Science ®Google Scholar
• Zhang H. Chen X. H. 2013 Seismic data reconstruction based on jittered sampling and curvelet transform: Chinese Journal of Geophysics 56 1637 1649 [in Chinese]
   Web of Science ®Google Scholar
• Zhang H. Chen X. H. Li H. X. 2015 3D seismic data reconstruction based on complex-valued curvelet transform in frequency domain: Journal of Applied Geophysics 113 64 73 10.1016/j.jappgeo.2014.12.004
   Web of Science ®Google Scholar
• Zhang H. Chen X. H. Zhang L. Y. 2017 3D simultaneous seismic data reconstruction and noise suppression based on the curvelet transform: Applied Geophysics 14 87 95 10.1007/s11770-017-0607-z
   Web of Science ®Google Scholar
• Zwartjes, P. M., 2005, Fourier reconstruction with sparse inversion: Ph.D. thesis, Delft University of Technology.
   Google Scholar