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Seismic data reconstruction via matrix completion
1. | Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095, United States |
2. | Department of Mathematics, Harbin Institute of Technology, Harbin, China |
3. | Department of Mathematics, University of California, Los Angeles, CA 90095 |
References:
[1] |
M. Sacchi, T. Ulrych and C. Walker, Interpolation and extrapolation using a high-resolution discrete fourier transform, IEEE Transactions on Signal Processing, 46 (1998), 31-38.
doi: 10.1109/78.651165. |
[2] |
A. Duijndam, M. Schonewille and C. Hindriks, Reconstruction of band-limited signals, irregularly sampled along one spatial direction, Geophysics, 64 (1999), 524-538.
doi: 10.1190/1.1444559. |
[3] |
B. Liu and M. D. Sacchi, Minimum weighted norm interpolation of seismic records, Geophysics, 69 (2004), 1560-1568.
doi: 10.1190/1.1836829. |
[4] |
S. Xu, Y. Zhang, D. L. Pham and G. Lambaré, Antileakage Fourier transform for seismic data regularization, Geophysics, 70 (2005), V87-V95.
doi: 10.1190/1.1993713. |
[5] |
F. J. Herrmann and G. Hennenfent, Non-parametric seismic data recovery with curvelet frames, Geophysical Journal International, 173 (2008), 233-248.
doi: 10.1111/j.1365-246X.2007.03698.x. |
[6] |
R. Shahidi, G. Tang, J. Ma and F. J. Herrmann, Application of randomized sampling schemes to curvelet-based sparsity-promoting seismic data recovery, Geophysical Prospecting, 61(2013), 973-997.
doi: 10.1111/1365-2478.12050. |
[7] |
M. Naghizadeh and M. Sacchi, Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data, Geophysics, 75 (2010), WB189-WB202.
doi: 10.1190/1.3509468. |
[8] |
S. Hauser and J. Ma, Seismic data reconstruction via directional weighted shearlet-regularized inpainting, Preprint, TUK, 2012. |
[9] |
S. Spitz, Seismic trace interpolation in the f-x domain, Geophysics, 56 (1991), 785-794. |
[10] |
S. Crawley, J. Claerbout and R. Clapp, Interpolation with smoothly nonstationary prediction-error filters, in 69th Annual International Meeting, SEG, Expanded Abstracts, 1913-1916, 1999.
doi: 10.1190/1.1820707. |
[11] |
M. Porsani, Seismic trace interpolation using half-step prediction filters, Geophysics, 64 (1999), 1461-1467.
doi: 10.1190/1.1444650. |
[12] |
Y. Liu and S. Fomel, Seismic data interpolation beyond aliasing using regularized nonstationary autoegression, Geophysics, 76 (2011), V69-V77.
doi: 10.1190/geo2010-0231.1. |
[13] |
M. Naghizadeh and M. Sacchi, Seismic data reconstruction using multidimensional prediction filters, Geophysical Prospecting, 58 (2010), 157-173.
doi: 10.1111/j.1365-2478.2009.00805.x. |
[14] |
S. Trickett, L. Burroughs, A. Milton, L. Walton and R. Dack, Rank-reduction-based trace interpolation, 80th Annual meeting, SEG, Expanded Abstracts, (2010).
doi: 10.1190/1.3513645. |
[15] |
V. Oropeza and M. Sacchi, Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis, Geophysics, 76 (2011), V25-V32.
doi: 10.1190/1.3552706. |
[16] |
R. Vautard and M. Ghil, Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series, Physica D, 35 (1989), 395-424.
doi: 10.1016/0167-2789(89)90077-8. |
[17] |
E. J. Candes and B. Recht, Exact matrix completion via convex optimization, Foundations of Computational Mathematics, 9 (2009), 717-772.
doi: 10.1007/s10208-009-9045-5. |
[18] |
H. Ji, C. Liu, Z. Shen and Y. Xu, Robust video denoising using low rank matrix completion, in Computer Vision and Pattern Recognition (CVPR), 2010 IEEE Conference, June 2010.
doi: 10.1109/CVPR.2010.5539849. |
[19] |
J.-F. Cai, E. J. Candes and Z. Shen, A singular value thresholding algorithm for matrix completion, SIAM Journal on Optimization, 20 (2008), 1956-1982.
doi: 10.1137/080738970. |
[20] |
S. Ma, D. Goldfarb and L. Chen, Fixed point and bregman iterative methods for matrix rank minimization, Mathematical Programming: Series A and B, 128 (2011), 321-353.
doi: 10.1007/s10107-009-0306-5. |
[21] |
J. Yang and X. Yuan, An inexact alternating direction method for trace norm regularized least squares problem, Optimization Online, (2010). |
[22] |
R. Keshavan, A. Montanari and S.Oh, Matrix completion from a few entries, IEEE Transactions on Information Theory, 56 (2010), 2980-2998.
doi: 10.1109/TIT.2010.2046205. |
[23] |
Y. Nesterov, A method of solving a convex programming problem with convergence rate o($1/k^2$), Soviet Mathematics Doklady, 27 (1983), 372-376. |
[24] |
A. Beck and M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM Journal on Imaging Sciences, (2009), 183-202.
doi: 10.1137/080716542. |
[25] |
K.-C. Toh and S. Yun, An advanced proximal gradient algorithm for nuclear norm regularized linear least squares problems, Pac. J. Optim., 6 (2010), 615-640. |
[26] |
Z. Wen, W. Yin and Y. Zhang, Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm, Mathematical Programming Computation, 4 (2012), 333-361.
doi: 10.1007/s12532-012-0044-1. |
[27] |
H. Schaeffer and S. Osher, A low patch-rank interpretation of texture, SIAM J. Imaging Sci., 6 (2013), 226-262.
doi: 10.1137/110854989. |
[28] |
Y. Hua, Estimating two-dimensional frequencies by matrix enhancement and matrix pencil, IEEE Transactions on Signal Processing, 40 (1992), 2267-2280. |
show all references
References:
[1] |
M. Sacchi, T. Ulrych and C. Walker, Interpolation and extrapolation using a high-resolution discrete fourier transform, IEEE Transactions on Signal Processing, 46 (1998), 31-38.
doi: 10.1109/78.651165. |
[2] |
A. Duijndam, M. Schonewille and C. Hindriks, Reconstruction of band-limited signals, irregularly sampled along one spatial direction, Geophysics, 64 (1999), 524-538.
doi: 10.1190/1.1444559. |
[3] |
B. Liu and M. D. Sacchi, Minimum weighted norm interpolation of seismic records, Geophysics, 69 (2004), 1560-1568.
doi: 10.1190/1.1836829. |
[4] |
S. Xu, Y. Zhang, D. L. Pham and G. Lambaré, Antileakage Fourier transform for seismic data regularization, Geophysics, 70 (2005), V87-V95.
doi: 10.1190/1.1993713. |
[5] |
F. J. Herrmann and G. Hennenfent, Non-parametric seismic data recovery with curvelet frames, Geophysical Journal International, 173 (2008), 233-248.
doi: 10.1111/j.1365-246X.2007.03698.x. |
[6] |
R. Shahidi, G. Tang, J. Ma and F. J. Herrmann, Application of randomized sampling schemes to curvelet-based sparsity-promoting seismic data recovery, Geophysical Prospecting, 61(2013), 973-997.
doi: 10.1111/1365-2478.12050. |
[7] |
M. Naghizadeh and M. Sacchi, Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data, Geophysics, 75 (2010), WB189-WB202.
doi: 10.1190/1.3509468. |
[8] |
S. Hauser and J. Ma, Seismic data reconstruction via directional weighted shearlet-regularized inpainting, Preprint, TUK, 2012. |
[9] |
S. Spitz, Seismic trace interpolation in the f-x domain, Geophysics, 56 (1991), 785-794. |
[10] |
S. Crawley, J. Claerbout and R. Clapp, Interpolation with smoothly nonstationary prediction-error filters, in 69th Annual International Meeting, SEG, Expanded Abstracts, 1913-1916, 1999.
doi: 10.1190/1.1820707. |
[11] |
M. Porsani, Seismic trace interpolation using half-step prediction filters, Geophysics, 64 (1999), 1461-1467.
doi: 10.1190/1.1444650. |
[12] |
Y. Liu and S. Fomel, Seismic data interpolation beyond aliasing using regularized nonstationary autoegression, Geophysics, 76 (2011), V69-V77.
doi: 10.1190/geo2010-0231.1. |
[13] |
M. Naghizadeh and M. Sacchi, Seismic data reconstruction using multidimensional prediction filters, Geophysical Prospecting, 58 (2010), 157-173.
doi: 10.1111/j.1365-2478.2009.00805.x. |
[14] |
S. Trickett, L. Burroughs, A. Milton, L. Walton and R. Dack, Rank-reduction-based trace interpolation, 80th Annual meeting, SEG, Expanded Abstracts, (2010).
doi: 10.1190/1.3513645. |
[15] |
V. Oropeza and M. Sacchi, Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis, Geophysics, 76 (2011), V25-V32.
doi: 10.1190/1.3552706. |
[16] |
R. Vautard and M. Ghil, Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series, Physica D, 35 (1989), 395-424.
doi: 10.1016/0167-2789(89)90077-8. |
[17] |
E. J. Candes and B. Recht, Exact matrix completion via convex optimization, Foundations of Computational Mathematics, 9 (2009), 717-772.
doi: 10.1007/s10208-009-9045-5. |
[18] |
H. Ji, C. Liu, Z. Shen and Y. Xu, Robust video denoising using low rank matrix completion, in Computer Vision and Pattern Recognition (CVPR), 2010 IEEE Conference, June 2010.
doi: 10.1109/CVPR.2010.5539849. |
[19] |
J.-F. Cai, E. J. Candes and Z. Shen, A singular value thresholding algorithm for matrix completion, SIAM Journal on Optimization, 20 (2008), 1956-1982.
doi: 10.1137/080738970. |
[20] |
S. Ma, D. Goldfarb and L. Chen, Fixed point and bregman iterative methods for matrix rank minimization, Mathematical Programming: Series A and B, 128 (2011), 321-353.
doi: 10.1007/s10107-009-0306-5. |
[21] |
J. Yang and X. Yuan, An inexact alternating direction method for trace norm regularized least squares problem, Optimization Online, (2010). |
[22] |
R. Keshavan, A. Montanari and S.Oh, Matrix completion from a few entries, IEEE Transactions on Information Theory, 56 (2010), 2980-2998.
doi: 10.1109/TIT.2010.2046205. |
[23] |
Y. Nesterov, A method of solving a convex programming problem with convergence rate o($1/k^2$), Soviet Mathematics Doklady, 27 (1983), 372-376. |
[24] |
A. Beck and M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM Journal on Imaging Sciences, (2009), 183-202.
doi: 10.1137/080716542. |
[25] |
K.-C. Toh and S. Yun, An advanced proximal gradient algorithm for nuclear norm regularized linear least squares problems, Pac. J. Optim., 6 (2010), 615-640. |
[26] |
Z. Wen, W. Yin and Y. Zhang, Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm, Mathematical Programming Computation, 4 (2012), 333-361.
doi: 10.1007/s12532-012-0044-1. |
[27] |
H. Schaeffer and S. Osher, A low patch-rank interpretation of texture, SIAM J. Imaging Sci., 6 (2013), 226-262.
doi: 10.1137/110854989. |
[28] |
Y. Hua, Estimating two-dimensional frequencies by matrix enhancement and matrix pencil, IEEE Transactions on Signal Processing, 40 (1992), 2267-2280. |
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