@conference {alfaraj2017SEGrsw,
	title = {Reconstruction of S-waves from low-cost randomized and simultaneous acquisition by joint sparse inversion},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2017},
	note = {(SEG, Houston)},
	month = {09},
	pages = {2533-2538},
	abstract = {Spatial Nyquist sampling rate, which is proportional to the apparent subsurface velocity, is the key deciding cost factor for conventional seismic acquisition. Due to the lower shear wave velocity compared with compressional waves, finer spatial sampling is required to properly record the earlier, which increases the acquisition costs. This is one of the reasons why shear waves are usually not considered in practice. To avoid having the Nyquist criterion as the deciding cost factor and to utilize multicomponent data to its available full extent, we propose acquiring randomly undersampled ocean bottom seismic data. Each component can then be interpolated separately, followed by elastic decomposition to recover up- and down-going S-waves. Instead, we jointly interpolate and decompose the recorded multicomponent data by solving one sparsity promoting optimization problem. This way we ensure that the relative amplitudes of the multicomponent data is preserved. We compare two sparsifying transforms: the curvelet transform and the frequency-wavenumber transform. Another key cost deciding factor for seismic acquisition is the efficiency of acquiring data. This calls for simultaneous acquisition, which requires a source separation step. Similarly, instead of taking a two-step approach, we perform a sparsity-promoting joint source separation decomposition. Results on economically and efficiently acquired synthetic data of both joint methods show their ability of reconstructing accurate up- and down-going S-waves.},
	keywords = {decomposition, elastic, interpolation, randomized acquisition, SEG, shear wave, source separation, sparse},
	doi = {10.1190/segam2017-17681376.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/alfaraj2017SEGrsw/alfaraj2017SEGrsw.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/alfaraj2017SEGrsw/alfaraj2017SEGrsw_pres.pdf},
	author = {Ali M. Alfaraj and Rajiv Kumar and Felix J. Herrmann}
}
@conference {alfaraj2017EAGEswr,
	title = {Shear wave reconstruction from low cost randomized acquisition},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2017},
	note = {(EAGE, Paris)},
	month = {06},
	abstract = {Shear waves travel in the subsurface at a lower speed compared with compressional waves. Therefore, much finer spatial sampling is required to properly record the shear waves. This leads to higher acquisition costs which are typically avoided by designing surveys geared towards only compressional waves imaging. We propose using randomly under-sampled ocean bottom acquisition for recording both compressional and shear waves. The recorded multicomponent data is then interpolated using an SVD-free low rank interpolation scheme that is feasible for large scale seismic data volumes to obtain finely sampled data. Following that, we perform elastic wavefield decomposition at the ocean bottom to recover accurate up- and dow-going S-waves. Synthetic data results indicate that using randomized under-sampled acquisition, we can recover accurate S-waves with an economical cost compared with conventional acquisition designs.},
	keywords = {EAGE, interpolation, randomized acquisition, rank minimization, shear waves},
	doi = {10.3997/2214-4609.201700594},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2017/alfaraj2017EAGEswr/alfaraj2017EAGEswr.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2017/alfaraj2017EAGEswr/alfaraj2017EAGEswr_pres.pdf},
	author = {Ali M. Alfaraj and Rajiv Kumar and Felix J. Herrmann}
}
@article {kumar2014GEOPemc,
	title = {Efficient matrix completion for seismic data reconstruction},
	journal = {Geophysics},
	volume = {80},
	number = {5},
	year = {2015},
	note = {(Geophysics)},
	month = {09},
	pages = {V97-V114},
	abstract = {Despite recent developments in improved acquisition, seismic data often remain undersampled along source and receiver coordinates, resulting in incomplete data for key applications such as migration and multiple prediction. We have interpreted the missing-trace interpolation problem in the context of matrix completion (MC), and developed three practical principles for using low-rank optimization techniques to recover seismic data. Specifically, we strive for recovery scenarios wherein the original signal is low rank and the subsampling scheme increases the singular values of the matrix. We use an optimization program that restores this low-rank structure to recover the full volume. Omitting one or more of these principles can lead to poor interpolation results, as we found experimentally. In light of this theory, we compensate for the high-rank behavior of data in the source-receiver domain by using the midpoint-offset transformation for 2D data and a source-receiver permutation for 3D data to reduce the overall singular values. Simultaneously, to work with computationally feasible algorithms for large-scale data, we use a factorization-based approach to MC, which significantly speeds up the computations compared with repeated singular value decompositions without reducing the recovery quality. In the context of our theory and experiments, we also find that windowing the data too aggressively can have adverse effects on the recovery quality. To overcome this problem, we carried out our interpolations for each frequency independently while working with the entire frequency slice. The result is a computationally efficient, theoretically motivated framework for interpolating missing-trace data. Our tests on realistic 2D and 3D seismic data sets show that our method compares favorably in terms of computational speed and recovery quality with existing curvelet- and tensor-based techniques.},
	keywords = {2D, 3D, algorithm, interpolation, low-rank, signal processing},
	doi = {10.1190/geo2014-0369.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2015/kumar2014GEOPemc/kumar2014GEOPemc.pdf},
	url2 = {http://library.seg.org/doi/abs/10.1190/geo2014-0369.1},
	author = {Rajiv Kumar and Curt Da Silva and Okan Akalin and Aleksandr Y. Aravkin and Hassan Mansour and Ben Recht and Felix J. Herrmann}
}
@conference {kumar2015EAGEmcu,
	title = {Matrix completion on unstructured grids : 2-D seismic data regularization and interpolation},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2015},
	note = {(EAGE, Madrid)},
	month = {06},
	abstract = {Seismic data interpolation via rank-minimization techniques has been recently introduced in the seismic community. All the existing rank-minimization techniques assume the recording locations to be on a regular grid, e.g., sampled periodically, but seismic data are typically irregularly sampled along spatial axes. Other than the irregularity of the sampled grid, we often have missing data. In this paper, we study the effect of grid irregularity to conduct matrix completion on a regular grid for unstructured data. We propose an improvement of existing rank-minimization techniques to do regularization. We also demonstrate that we can perform seismic data regularization and interpolation simultaneously. We illustrate the advantages of the modification using a real seismic line from the Gulf of Suez to obtain high quality results for regularization and interpolation, a key application in exploration geophysics.},
	keywords = {EAGE, interpolation, matrix completion, NFFT, regularization},
	doi = {10.3997/2214-4609.201413448},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/kumar2015EAGEmcu/kumar2015EAGEmcu.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/kumar2015EAGEmcu/kumar2015EAGEmcu_poster.pdf},
	author = {Rajiv Kumar and Oscar Lopez and Ernie Esser and Felix J. Herrmann}
}
@conference {lopez2015EAGErma,
	title = {Rank minimization via alternating optimization: seismic data interpolation},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2015},
	note = {(EAGE, Madrid)},
	month = {06},
	abstract = {Low-rank matrix completion techniques have recently become an effective tool for seismic trace interpolation problems. In this talk, we consider an alternating optimization scheme for nuclear norm minimization and discuss the applications to large scale wave field reconstruction. By adopting a factorization approach to the rank minimization problem we write our low-rank matrix in bi-linear form, and modify this workflow by alternating our optimization to handle a single matrix factor at a time. This allows for a more tractable procedure that can robustly handle large scale, highly oscillatory and critically subsampled seismic data sets. We demonstrate the potential of this approach with several numerical experiments on a seismic line from the Nelson 2D data set and a frequency slice from the Gulf of Mexico data set.},
	keywords = {EAGE, interpolation, low-rank, matrix completion},
	doi = {10.3997/2214-4609.201413453},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/lopez2015EAGErma/lopez2015EAGErma.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/lopez2015EAGErma/lopez2015EAGErma_poster.pdf},
	author = {Oscar Lopez and Rajiv Kumar and Felix J. Herrmann}
}
@conference {lopez2015SEGWSsfm,
	title = {SVD-free matrix completion in randomized marine acquisition},
	booktitle = {SEG Workshop on Rank-Reduction and Other Sparse Transform Methods with Application to Data Reconstruction, De-Noising, De-Blending and Imaging; New Orleans},
	year = {2015},
	note = {(SEG, New Orleans)},
	month = {10},
	abstract = {During this presentation, we will illustrate how insights from matrix-free matrix completion can be used to solve problems in (on- and off-the-grid) missing trace interpolation and time-jittered (simultaneous) marine acquisition. In particular, we will demonstrate the importance of data organization to favor recovery by rank minimization and the use of deterministic spectral properties to predict the recovery. We also make make comparisons between wavefield reconstructions based on transform-domain sparsity promotion and matrix completion.},
	keywords = {Acquisition, interpolation, matrix completion, rank reduction, SEG, workshop},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2015/lopez2015SEGWSsfm/lopez2015SEGWSsfm_pres.pdf},
	author = {Oscar Lopez and Haneet Wason and Curt Da Silva and Rajiv Kumar and Felix J. Herrmann}
}
@techreport {kumar2014SEGmcu,
	title = {Matrix completion on unstructured grids : 2-D seismic data regularization and interpolation},
	number = {TR-EOAS-2014-3},
	year = {2014},
	month = {04},
	institution = {UBC},
	abstract = {Seismic data interpolation via rank-minimization techniques has been recently introduced in the seismic community. All the existing rank-minimization techniques assume the recording locations to be on a regular grid, e.g. sampled periodically, but seismic data are typically irregularly sampled along spatial axes. Other than the irregularity of the sampled grid, we often have missing data. In this paper, we study the effect of grid irregularity to conduct matrix completion on a regular grid for unstructured data. We propose an improvement of existing rank-minimization techniques to do regularization. We also demonstrate that we can perform seismic data regularization and interpolation simultaneously. We illustrate the advantages of the modification using a real seismic line from the Gulf of Suez to obtain high quality results for regularization and interpolation, a key application in exploration geophysics.},
	keywords = {interpolation, matrix completion, NFFT, regularization},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2014/kumar2014SEGmcu/kumar2014SEGmcu.html},
	author = {Rajiv Kumar and Oscar Lopez and Ernie Esser and Felix J. Herrmann}
}
@conference {kumar2014EAGErank,
	title = {SVD-free low-rank matrix factorization : wavefield reconstruction via jittered subsampling and reciprocity},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2014},
	month = {06},
	abstract = {Recently computationally efficient rank optimization techniques have been studied extensively to develop a new mathematical tool for the seismic data interpolation. So far, matrix completion problems have been discussed where sources are subsample according to a discrete uniform distribution. In this paper, we studied the effect of two different subsampling techniques on seismic data interpolation using rank-regularized formulations, namely jittered subsampling over uniform random subsampling. The other objective of this paper is to combine the fact of source-receiver reciprocity with the rank-minimization techniques to enhance the accuracy of missing-trace interpolation. We illustrate the advantages of jittered subsampling and reciprocity using a seismic line from Gulf of Suez to obtain high quality results for interpolation, a key application in exploration geophysics.},
	keywords = {EAGE, interpolation, low-rank, reciprocity},
	doi = {10.3997/2214-4609.20141394},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/kumar2014EAGErank/kumar2014EAGErank.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/kumar2014EAGErank/kumar2014EAGErank_pres.pdf},
	author = {Rajiv Kumar and Aleksandr Y. Aravkin and Ernie Esser and Hassan Mansour and Felix J. Herrmann}
}
@conference {kumar2013SEGHSS,
	title = {Reconstruction of seismic wavefields via low-rank matrix factorization in the hierarchical-separable matrix representation},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {32},
	year = {2013},
	month = {09},
	pages = {3628-3633},
	abstract = {Recent developments in matrix rank optimization have allowed for new computational approaches in the field of seismic data interpolation. In this paper, we propose an approach for seismic data interpolation which incorporates the Hierarchical Semi-Separable Structure (HSS) inside rank-regularized least-squares formulations for the missing-trace interpolation problem. The proposed approach is suitable for large scale problems, since it avoids SVD computations and uses a low-rank factorized formulation instead. We illustrate the advantages of the new HSS approach by interpolating a seismic line from the Gulf of Suez and compare the reconstruction with conventional rank minimization.},
	keywords = {HSS, interpolation, SEG},
	doi = {10.1190/segam2013-1165.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/kumar2013SEGHSS/kumar2013SEGHSS.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/kumar2013SEGHSS/kumar2013SEGHSS_pres.pdf},
	author = {Rajiv Kumar and Hassan Mansour and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@conference {kumar2013EAGEsind,
	title = {Seismic data interpolation and denoising using SVD-free low-rank matrix factorization},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2013},
	month = {06},
	abstract = {Recent developments in rank optimization have allowed new approaches for seismic data interpolation and denoising. In this paper, we propose an approach for simultaneous seismic data interpolation and denoising using robust rank-regularized formulations. The proposed approach is suitable for large scale problems, since it avoids SVD computations by using factorized formulations. We illustrate the advantages of the new approach using a seismic line from Gulf of Suez and 5D synthetic seismic data to obtain high quality results for interpolation and denoising, a key application in exploration geophysics.},
	keywords = {denoising, EAGE, interpolation},
	doi = {10.3997/2214-4609.20130388},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2013/kumar2013EAGEsind/kumar2013EAGEsind.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2013/kumar2013EAGEsind/kumar2013EAGEsind_pres.pdf},
	author = {Rajiv Kumar and Aleksandr Y. Aravkin and Hassan Mansour and Ben Recht and Felix J. Herrmann}
}
@techreport {kumar2013ICMLlr,
	title = {An SVD-free Pareto curve approach to rank minimization},
	number = {TR-EOAS-2013-2},
	year = {2013},
	month = {02},
	institution = {UBC},
	abstract = {Recent SVD-free matrix factorization formulations have enabled rank optimization for extremely large-scale systems (millions of rows and columns). In this paper, we consider rank-regularized formulations that only require a target data-fitting error level, and propose an algorithm for the corresponding problem. We illustrate the advantages of the new approach using the Netflix problem, and use it to obtain high quality results for seismic trace interpolation, a key application in exploration geophysics. We show that factor rank can be easily adjusted as the inversion proceeds, and propose a weighted extension that allows known subspace information to improve the results of matrix completion formulations. Using these methods, we obtain high-quality reconstructions for large scale seismic interpolation problems with real data.},
	keywords = {interpolation, low rank},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2013/kumar2013ICMLlr/kumar2013ICMLlr.pdf},
	author = {Aleksandr Y. Aravkin and Rajiv Kumar and Hassan Mansour and Ben Recht and Felix J. Herrmann}
}
