@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}
}
@presentation {aravkin2012SINBADenp,
	title = {Estimating nuisance parameters in inverse problems},
	year = {2012},
	publisher = {SINBAD},
	abstract = {Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. In this talk, we present the idea of "projecting out" these variables, and how this idea allows us to design methods for solving a broad class of problems with nuisance parameters, such as variance or degrees of freedom. We then discuss several geophysical applications, including including estimation of unknown variance parameters in the Gaussian model for full waveform inversion, degree of freedom (d.o.f.) parameter estimation in the context of robust imaging problems, and robust source estimation.},
	keywords = {Presentation, SINBAD, SINBADFALL2012, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2012/Fall/aravkin2012SINBADenp/aravkin2012SINBADenp_pres.pdf},
	author = {Aleksandr Y. Aravkin}
}
@article {aravkin2012IPNuisance,
	title = {Estimating nuisance parameters in inverse problems},
	journal = {Inverse Problems},
	volume = {28},
	number = {11},
	year = {2012},
	month = {10},
	abstract = {Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is variable projection, where nonlinear least squares problems which are linear in some parameters can be very efficiently optimized. In this paper, we extend the idea of projecting out a subset over the variables to a broad class of maximum likelihood (ML) and maximum a posteriori likelihood (MAP) problems with nuisance parameters, such as variance or degrees of freedom. As a result, we are able to incorporate nuisance parameter estimation into large-scale constrained and unconstrained inverse problem formulations. We apply the approach to a variety of problems, including estimation of unknown variance parameters in the Gaussian model, degree of freedom (d.o.f.) parameter estimation in the context of robust inverse problems, automatic calibration, and optimal experimental design. Using numerical examples, we demonstrate improvement in recovery of primary parameters for several large- scale inverse problems. The proposed approach is compatible with a wide variety of algorithms and formulations, and its implementation requires only minor modifications to existing algorithms.},
	keywords = {full waveform inversion, students t, variance},
	doi = {10.1088/0266-5611/28/11/115016},
	url = {http://arxiv.org/abs/1206.6532},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/InverseProblems/2012/aravkin2012IPNuisance/aravkin2012IPNuisance.pdf},
	author = {Aleksandr Y. Aravkin and Tristan van Leeuwen}
}
@presentation {aravkin2011SINBADesp,
	title = {Extensions to sparsity promotion},
	year = {2011},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2011, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2011/Fall/aravkin2011SINBADesp/aravkin2011SINBADesp_pres.pdf},
	author = {Aleksandr Y. Aravkin}
}
@presentation {aravkin2010SINBADesf,
	title = {Exploiting sparsity in full-waveform inversion: nonlinear basis pursuit denoise algorithm},
	year = {2010},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2010, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2010/Fall/aravkin2010SINBADesf/aravkin2010SINBADesf_pres.pdf},
	author = {Aleksandr Y. Aravkin}
}
