@conference {witte2019SIAMCSEclsmft,
	title = {Compressive least squares migration with on-the-fly Fourier transforms},
	booktitle = {SIAM Conference on Computational Science and Engineering},
	year = {2019},
	note = {(SIAM CSE)},
	month = {03},
	abstract = {Least-squares seismic imaging is an inversion-based approach for accurately imaging the earth{\textquoteright}s subsurface. However, in the time-domain, the computational cost and memory requirements of this approach scale with the size and recording length of the seismic experiment, thus making this approach often prohibitively expensive in practice. To overcome these issues, we borrow ideas from compressive sensing and signal processing and introduce an algorithm for sparsity-promoting seismic imaging using on-the-fly Fourier transforms. By computing gradients and functions values for random subsets of source locations and frequencies, we considerably limit the number of wave equation solves, while on-the-fly Fourier transforms allow computing an arbitrary number of monochromatic frequency-domain wavefields with a time-domain modeling code and without having to solve large-scale Helmholtz equations. The memory requirements of this approach are independent of the number of time steps and solely depend on the number of frequencies, which determine the amount of crosstalk and subsampling artifacts in the image. We show the application of our approach to several large-scale open source data sets and compare the results to a conventional time-domain approach with optimal checkpointing.},
	keywords = {Fourier, Imaging, least-squares, migration, on-the-fly},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SIAMCSE/2019/witte2019SIAMCSEclsmft/witte2019SIAMCSEclsmft.pdf},
	author = {Philipp A. Witte and Mathias Louboutin and Fabio Luporini and Gerard J. Gorman and Felix J. Herrmann}
}
@conference {peters2019SEGans,
	title = {A numerical solver for least-squares sub-problems in 3D wavefield reconstruction inversion and related problem formulations},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2019},
	note = {(SEG, San Antonio)},
	month = {09},
	pages = {1536-1540},
	abstract = {Recent years saw a surge of interest in seismic waveform inversion approaches based on quadratic-penalty or augmented-Lagrangian methods, including Wavefield Reconstruction Inversion. These methods typically need to solve a least-squares sub-problem that contains a discretization of the Helmholtz equation. Memory requirements for direct solvers are often prohibitively large in three dimensions, and this limited the examples in the literature to two dimensions. We present an algorithm that uses iterative Helmholtz solvers as a black-box to solve the least-squares problem corresponding to 3D grids. This algorithm enables Wavefield Reconstruction Inversion and related formulations, in three dimensions. Our new algorithm also includes a root-finding method to convert a penalty into a constraint on the data-misfit without additional computational cost, by reusing precomputed quantities. Numerical experiments show that the cost of parallel communication and other computations are small compared to the main cost of solving one Helmholtz problem per source and one per receiver.},
	keywords = {Full-waveform inversion, least-squares, numerical linear algebra, penalty method, quadratic constraints, root finding, SEG},
	doi = {10.1190/segam2019-3216638.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2019/peters2019SEGans/peters2019SEGans.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2019/peters2019SEGans/peters2019SEGans_pres.pdf},
	author = {Bas Peters and Felix J. Herrmann}
}
@conference {peters2015PRECONasl,
	title = {An algorithm for solving least-squares problems with a Helmholtz block and multiple right-hand-sides},
	booktitle = {International Conference On Preconditioning Techniques For Scientific And Industrial Applications},
	year = {2015},
	note = {(PRECON, The Netherlands)},
	month = {06},
	keywords = {CGMN, Helmholtz, least-squares, matrix-free, randomized linear algebra},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/PRECON/2015/peters2015PRECONasl/peters2015PRECONasl_pres.pdf},
	author = {Bas Peters and Chen Greif and Felix J. Herrmann}
}
@mastersthesis {tu2015THfis,
	title = {Fast imaging with surface-related multiples},
	year = {2015},
	note = {(PhD)},
	month = {08},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {Surface-related multiples, which are waves that bounce more than once between the water surface and the subsurface reflectors, constitute a significant part of the data acquired in marine seismic surveys. If left untreated, they can lead to misplaced phantom reflectors in the image, and result in erroneous interpretations of the subsurface structure. As a result, these multiples are removed before the imaging procedure in conventional seismic data processing. However, because they interact more with the subsurface medium, they may carry extra information that is not present in the primaries. Therefore instead of removing these multiples, a more desirable alternative is to make active use of them. We derive from the well-established "Surface-Related Multiple Elimination" relation, and arrive at a linearized expression of the wave-equation based modelling that incorporates the surface- related multiples. We then present a computationally efficient approach to iteratively invert this expression to obtain an image of the subsurface from data that contain multiples. We achieve the computational efficiency inside each iteration by (i) using the wave-equation solver to implicitly carry out the expensive multiple prediction; and (ii) reducing the number of wave-equation solves during data simulation by subsampling the monochromatic source experiments. We show that, compared with directly applying the cross-correlation/deconvolutional imaging conditions, the presented approach can suppress the coherent imaging artifacts from multiples more effectively. We also show that, by curvelet-domain sparsity promoting and occasionally drawing new data samples during the inversion, the proposed inversion method gains improved robustness to velocity errors in the background model, as well as modelling errors incurred during linearization of the wave-equation. To combine the information encoded in both the primaries and the multiples, we then propose a highly accurate source estimation method to jointly invert the total upgoing wavefield. We show with field data examples that we can reap benefits from both the relative noise-free primaries and the extra illumination coverage of the multiples. We also demonstrate that the inclusion of multiples help mitigate the amplitude ambiguity during source estimation. We conclude the thesis with an outlook for future research directions, as well as potential extensions of the proposed work.},
	keywords = {inversion, least-squares, multiples, seismic imaging},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2015/tu2015THfis/tu2015THfis.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2015/tu2015THfis/tu2015THfis_pres.pdf},
	author = {Ning Tu}
}
@conference {peters2015SIAMmfq,
	title = {Matrix-free quadratic-penalty methods for PDE-constrained optimization},
	booktitle = {SIAM Conference on Computational Science and Engineering},
	year = {2015},
	note = {(SIAM, Salt Lake City)},
	month = {03},
	abstract = {The large scale of seismic waveform inversion makes matrix free implementations essential. We show how to exploit the quadratic penalty structure to construct matrix free reduced-space and full-space algorithms, which have some advantages over the commonly used Lagrangian based methods for PDE-constrained optimization. This includes the construction of effective and sparse Hessian approximations and reduced sensitivity to the initial guess. A computational bottleneck is the need to solve a large least squares problem with a PDE block. When direct solvers are not available, we propose a fast matrix free iterative approach with reasonable memory requirements. It takes advantage of the structure of the least squares problem with a combination of preconditioning, low rank decomposition and deflation.},
	keywords = {least-squares, low-rank, PDE-constrained optimization, quadratic-penalty, waveform inversion},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2015/peters2015SIAMmfq/peters2015SIAMmfq.pdf},
	author = {Bas Peters and Felix J. Herrmann and Chen Greif}
}
@conference {li2013SEGodmvdaiedwawe,
	title = {Optimization driven model-space versus data-space approaches to invert elastic data with the acoustic wave equation},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {32},
	year = {2013},
	month = {09},
	pages = {986-990},
	abstract = {Inverting data with elastic phases using an acoustic wave equation can lead to erroneous results, especially when the number of iterations is too high, which may lead to over fitting the data. Several approaches have been proposed to address this issue. Most commonly, people apply "data-independent" filtering operations that are aimed to deemphasize the elastic phases in the data in favor of the acoustic phases. Examples of this approach are nested loops over offset range and Laplace parameters. In this paper, we discuss two complementary optimization-driven methods where the minimization process decides adaptively which of the data or model components are consistent with the objective. Specifically, we compare the Student{\textquoteright}s t misfit function as the data-space alternative and curvelet-domain sparsity promotion as the model-space alternative. Application of these two methods to a realistic synthetic lead to comparable results that we believe can be improved by combining these two methods.},
	keywords = {elastic, Full-waveform inversion, least-squares, SEG},
	doi = {10.1190/segam2013-1375.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/li2013SEGodmvdaiedwawe/li2013SEGodmvdaiedwawe.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/li2013SEGodmvdaiedwawe/li2013SEGodmvdaiedwawe_pres.pdf},
	author = {Xiang Li and Anais Tamalet and Tristan van Leeuwen and Felix J. Herrmann}
}
