@article {rizzuti2020dfw,
	title = {A dual formulation of wavefield reconstruction inversion for large-scale seismic inversion},
	journal = {Geophysics},
	volume = {86},
	number = {6},
	year = {2021},
	note = {(Geophysics)},
	month = {10},
	pages = {1ND-Z3},
	abstract = {Many of the seismic inversion techniques currently proposed that focus on robustness with respect to the background model choice are not apt to large-scale 3D applications, and the methods that are computationally feasible for industrial problems, such as full waveform inversion, are notoriously limited by convergence stagnation and require adequate starting models. We propose a novel solution that is both scalable and less sensitive to starting models or inaccurate parameters (such as anisotropy) that are typically kept fixed during inversion. It is based on a dual reformulation of the classical wavefield reconstruction inversion, whose empirical robustness with respect to these issues is well documented in the literature. While the classical version is not suited to 3D, as it leverages expensive frequency-domain solvers for the wave equation, our proposal allows the deployment of state-of-the-art time-domain finite-difference methods, and is potentially mature for industrial-scale problems.},
	keywords = {3D, finite-difference, Full-waveform inversion, wave equation},
	doi = {10.1190/geo2020-0743.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2021/rizzuti2020dfw/rizzuti2020dfw.html},
	author = {Gabrio Rizzuti and Mathias Louboutin and Rongrong Wang and Felix J. Herrmann}
}
@conference {rizzuti2020EAGEtwri,
	title = {Time-domain wavefield reconstruction inversion for large-scale seismics},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2020},
	note = {Accepted in EAGE, withdrawn due to logistical challenge},
	month = {1},
	abstract = {Wavefield reconstruction inversion is an imaging technique akin to full-waveform inversion, albeit based on a relaxed version of the wave equation. This relaxation aims to beat the multimodality typical of full-waveform inversion. However it prevents the use of time-marching solvers for the augmented equation and, as a consequence, cannot be straightforwardly employed to large 3D problems. In this work, we formulate a dual version of wavefield reconstruction inversion amenable to explicit time-domain solvers, yielding a robust and scalable inversion technique.},
	keywords = {3D, EAGE, Full-waveform inversion, Time-domain},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2020/rizzuti2020EAGEtwri/rizzuti2020EAGEtwri.html},
	author = {Gabrio Rizzuti and Mathias Louboutin and Rongrong Wang and Felix J. Herrmann}
}
@conference {rizzuti2019SEGadf,
	title = {A dual formulation for time-domain wavefield reconstruction inversion},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2019},
	note = {(SEG, San Antonio)},
	month = {09},
	pages = {1480-1485},
	abstract = {We illustrate a dual formulation for full-waveform inversion potentially apt to large 3-D problems. It is based on the optimization of the wave equation compliance, under the constraint of data misfit not exceeding a prescribed noise level. In the Lagrangian formulation, model and wavefield state variables are complemented with multipliers having the same dimension of data ("dual data" variables). Analogously to classical wavefield reconstruction inversion, the wavefield unknowns can be projected out in closed form, by solving a version of the augmented wave equation. This leads to a saddle-point problem whose variables are only model and dual data. As such, this formulation represents a model extension, and is potentially robust against local minima. The classical downsides of model extension methods and wavefield reconstruction inversion are here effectively mitigated: storage of the dual variables is affordable, the augmented wave equation is amenable to time-marching finite-difference schemes, and no continuation strategy for penalty parameters is needed, with the prospect of 3-D applications.},
	keywords = {3D, Full-waveform inversion, SEG, Time-domain},
	doi = {10.1190/segam2019-3216760.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2019/rizzuti2019SEGadf/rizzuti2019SEGadf.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2019/rizzuti2019SEGadf/rizzuti2019SEGadf_pres.pdf},
	software = {https://github.com/slimgroup/Software.rizzuti2019SEGadf},
	author = {Gabrio Rizzuti and Mathias Louboutin and Rongrong Wang and Emmanouil Daskalakis and Felix J. Herrmann}
}
@article {liu2018ssi,
	title = {Simultaneous-shot inversion for PDE-constrained optimization problems with missing data},
	journal = {Inverse Problems},
	volume = {35},
	number = {2},
	year = {2018},
	note = {(Inverse Problems)},
	pages = {025003},
	abstract = {Stochastic optimization is key to efficient inversion in PDE-constrained optimization. Using {\textquoteleft}simultaneous shots{\textquoteright}, or random superposition of source terms, works very well in simple acquisition geometries where all sources see all receivers, but this rarely occurs in practice. We develop an approach that interpolates data to an ideal acquisition geometry while solving the inverse problem using simultaneous shots. The approach is formulated as a joint inverse problem, combining ideas from low-rank interpolation with full-waveform inversion. Results using synthetic experiments illustrate the flexibility and efficiency of the approach.},
	keywords = {Full-waveform inversion, low-rank interpolation, Optimization},
	doi = {10.1088/1361-6420/aaf317},
	url = {https://slim.gatech.edu/Publications/Public/Journals/InverseProblems/2018/liu2018ssi/liu2018ssi.pdf},
	author = {Michelle Liu and Rajiv Kumar and Eldad Haber and Aleksandr Y. Aravkin}
}
@conference {witte2017SIAMlsw,
	title = {Large-scale workflows for wave-equation based inversion in Julia},
	booktitle = {SIAM Conference on Computational Science and Engineering},
	year = {2017},
	note = {(SIAM Conference on Computational Science and Engineering, Atlanta)},
	month = {02-03},
	abstract = {Full-waveform inversion is a PDE-constrained optimisation problem involving massive amounts of data (petabytes) and large numbers of unknowns (O(10^9)). This well known compute-intensive and data-intensive is extremely challenging for several reasons. First, there is the complexity of having to handle extremely large data volumes with metadata related to experimental details in the field, and the discretization of the unknown earth parameters and approximate physics. Second, reduced or adjoint-state methods call for computationally intensive PDE solves for each source experiment (of which there are thousands) for each iteration of a gradient-based optimization scheme. The talks will give an overview how carefully chosen layers of abstraction can help manage both the complexity and scale of inversion while still achieving the high degree of computational performance required to make full-waveform a practical tool. Specifically, the presentations will focus on domain specific stencil language for time-stepping methods to solve various types of wave equations and on abstracts for large-scale parallel optimization frameworks.},
	keywords = {Full-waveform inversion, Julia, large scale, least-squares migration, SIAM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2017/witte2017SIAMlsw/witte2017SIAMlsw_pres.mov},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2017/witte2017SIAMlsw/witte2017SIAMlsw_pres.pdf},
	author = {Philipp A. Witte and Mathias Louboutin and Felix J. Herrmann}
}
@conference {deaguiar2016SCdff,
	title = {DeVito: fast finite difference computation},
	booktitle = {Super Computing (SC16)},
	year = {2016},
	note = {(Super Computing, Utah)},
	month = {11},
	abstract = {Seismic imaging, used in energy exploration, is arguably the most compute and data intensive application in the private sector. The commonly used methods involve solving the wave equations numerically using finite difference formulations. Writing optimized code for these applications involves multiple man-years of effort that need to be repeated every time a new development needs to be factored in {\textendash} for every target platform. DeVito is a new tool for performing optimized Finite Difference (FD) computation from high-level symbolic problem definitions. The application developer needs to provide a differential equation in symbolic form. DeVito performs automated code generation and Just-In-Time (JIT) compilation based on this symbolic equation to create and execute highly optimized Finite Difference kernels on multiple computer platforms. DeVito has been designed to be used as part of complex workflows involving data flows across multiple applications over different nodes of a cluster.},
	keywords = {finite differences, Full-waveform inversion, high performance computing},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SC/2016/deaguiar2016SCdff/deaguiar2016SCdff_poster.pdf},
	url2 = {http://sc16.supercomputing.org/sc-archive/tech_poster/tech_poster_pages/post155.html},
	author = {Marcos de Aguiar and Gerard Gorman and Felix J. Herrmann and Navjot Kukreja and Michael Lange and Mathias Louboutin and Felippe Vieira Zacarias}
}
@article {li2015GEOPmgn,
	title = {Modified Gauss-Newton full-waveform inversion explained{\textendash}-why sparsity-promoting updates do matter},
	journal = {Geophysics},
	volume = {81},
	number = {3},
	year = {2016},
	note = {(Geophysics)},
	month = {05},
	pages = {R125-R138},
	abstract = {Full-waveform inversion can be formulated as a nonlinear least-squares optimization problem. This non-convex problem can be extremely computationally expensive because it requires repeatedly solving large linear systems that correspond to discretized partial differential equations. Randomized subsampling techniques allow us to work with small subsets of (monochromatic) source experiments, reducing the computational cost. However, this subsampling weakens subsurface illumination and introduces subsampling related incoherent artifacts. These subsampling-related artifacts{\textendash}-in conjunction with local minima that are known to plague full-waveform inversion{\textendash}-motivate us to come up with a technique to "regularize" this problem. Following earlier work, we take advantage of the fact that curvelets represent subsurface models and perturbations parsimoniously. At first impulse promoting sparsity on the model directly seems the most natural way to proceed, but we will demonstrate that in certain cases it can be advantageous to promote sparsity on the Gauss-Newton updates instead. While constraining the one-norm of the descent directions does not change not change the underlying full-waveform inversion objective, the constrained model updates remain descent directions, remove subsampling-related artifacts and improve the overall inversion result. We empirically observe this phenomenon in situations where the different model updates occur at roughly the same locations in the curvelet domain. We further investigate and analyze this phenomenon, where nonlinear inversions benefit from sparsity-promoting constraints on the updates, by means of a set of carefully selected examples including phase retrieval and full-waveform inversion. In all cases, we observe a faster decay of the residual and model error as a function of the number of iterations.},
	keywords = {Full-waveform inversion, Gauss-Newton method, sparsity promotion},
	doi = {10.1190/geo2015-0266.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2016/li2015GEOPmgn/li2015GEOPmgn.pdf},
	author = {Xiang Li and Ernie Esser and Felix J. Herrmann}
}
@mastersthesis {li2015THsps,
	title = {Sparsity promoting seismic imaging and full-waveform inversion},
	year = {2015},
	note = {(PhD)},
	month = {07},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {This thesis will address the large computational costs of solving least-squares migration and full-waveform inversion problems. Least-squares seismic imaging and full-waveform inversion are seismic inversion techniques that require iterative minimizations of large least-squares misfit functions. Each iteration requires an evaluation of the Jacobian operator and its adjoint, both of which require two wave-equation solves for all sources, creating prohibitive computational costs. In order to reduce costs, we utilize randomized dimensionality reduction techniques, reducing the number of sources used during inversion. The randomized dimensionality reduction techniques create subsampling related artifacts, which we mitigate by using curvelet-domain sparsity-promoting inversion techniques. Our method conducts least-squares imaging at the approximate cost of one reverse-time migration with all sources, and computes the Gauss-Newton full-waveform inversion update at roughly the cost of one gradient update with all sources. Finally, during our research of the full-waveform inversion problem, we discovered that we can utilize our method as an alternative approach to add sparse constraints on the entire velocity model by imposing sparsity constraints on each model update separately, rather than regularizing the total velocity model as typically practiced. We also observed this alternative approach yields a faster decay of the residual and model error as a function of iterations. We provided empirical arguments why and when imposing sparsity on the updates can lead to improved full-waveform inversion results.},
	keywords = {Full-waveform inversion, Gauss-Newton method, least-squares imaging, seismic imaging, sparsity promoting},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2015/li2015THsps/li2015THsps.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2015/li2015THsps/li2015THsps_pres.pdf},
	author = {Xiang Li}
}
@conference {louboutin2015SEGtcs,
	title = {Time compressively sampled full-waveform inversion with stochastic optimization},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2015},
	note = {(SEG, New Orleans)},
	month = {10},
	pages = {5153-5157},
	abstract = {Time-domain Full-Waveform Inversion (FWI) aims to image the subsurface of the earth accurately from field recorded data and can be solved via the reduced adjoint-state method. However, this method requires access to the forward and adjoint wavefields that are meet when computing gradient updates. The challenge here is that the adjoint wavefield is computed in reverse order during time stepping and therefore requires storage or other type of mitigation because storing the full time history of the forward wavefield is too expensive in realistic 3D settings. To overcome this challenge, we propose an approximate adjoint-state method where the wavefields are subsampled randomly, which drastically the amount of storage needed. By using techniques from stochastic optimization, we control the errors induced by the subsampling. Examples of the proposed technique on a synthetic but realistic 2D model show that the subsampling-related artifacts can be reduced significantly by changing the sampling for each source after each model update. Combination of this gradient approximation with a quasi-Newton method shows virtually artifact free inversion results requiring only 5\% of storage compared to saving the history at Nyquist. In addition, we avoid having to recompute the wavefields as is required by checkpointing.},
	keywords = {acoustic, Full-waveform inversion, inversion, SEG, Stochastic optimization, Subsampling, Time-domain},
	doi = {10.1190/segam2015-5924937.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2015/louboutin2015SEGtcs/louboutin2015SEGtcs.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2015/louboutin2015SEGtcs/louboutin2015SEGtcs_poster.pdf},
	author = {Mathias Louboutin and Felix J. Herrmann}
}
@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}
}
@conference {herrmann2011SEGffw,
	title = {Fast full-waveform inversion with compressive sensing},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2011},
	keywords = {Full-waveform inversion, SEG, SLIM},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2011/HerrmannSEG2011fws/HerrmannSEG2011fws.pdf},
	author = {Aleksandr Y. Aravkin and Felix J. Herrmann and Tristan van Leeuwen and Xiang Li}
}
@conference {herrmann2011SLRAfwi,
	title = {Full waveform inversion with compressive updates},
	booktitle = {SLRA},
	year = {2011},
	publisher = {Sparse and Low Rank Approximation 2011},
	organization = {Sparse and Low Rank Approximation 2011},
	abstract = {Full-waveform inversion relies on large multi-experiment data volumes. While improvements in acquisition and inversion have been extremely successful, the current push for higher quality models reveals fundamental shortcomings handling increasing problem sizes numerically. To address this fundamental issue, we propose a randomized dimensionality-reduction strategy motivated by recent developments in stochastic optimization and compressive sensing. In this formulation conventional Gauss-Newton iterations are replaced by dimensionality-reduced sparse recovery problems with source encodings.},
	keywords = {Full-waveform inversion},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SLRA/2011/herrmann2011SLRAfwi/herrmann2011SLRAfwi.pdf},
	author = {Felix J. Herrmann and Aleksandr Y. Aravkin and Xiang Li and Tristan van Leeuwen}
}
@conference {aravkin2011SIAMfwi,
	title = {Full waveform inversion with compressive updates},
	booktitle = {SIAM},
	year = {2011},
	publisher = {SIAM CS\&E 2011},
	organization = {SIAM CS\&E 2011},
	abstract = {Full-waveform inversion relies on large multi-experiment data volumes. While improvements in acquisition and inversion have been extremely successful, the current push for higher quality models reveals fundamental shortcomings handling increasing problem sizes numerically. To address this fundamental issue, we propose a randomized dimensionality-reduction strategy motivated by recent developments in stochastic optimization and compressive sensing. In this formulation conventional Gauss-Newton iterations are replaced by dimensionality-reduced sparse recovery problems with source encodings.},
	keywords = {Full-waveform inversion, SLIM},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2011/aravkin2011SIAMfwi/aravkin2011SIAMfwi.pdf},
	author = {Aleksandr Y. Aravkin and Felix J. Herrmann and Tristan van Leeuwen and James V. Burke and Xiang Li}
}
@conference {li2011EAGEfwirr,
	title = {Full-waveform inversion with randomized L1 recovery for the model updates},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2011},
	month = {05},
	abstract = {Full-waveform inversion (FWI) is a data fitting procedure that relies on the collection of seismic data volumes and sophisticated computing to create high-resolution results. With the advent of FWI, the improvements in acquisition and inversion have been substantial, but these improvements come at a high cost because FWI involves extremely large multi-experiment data volumes. The main obstacle is the "curse of dimensionality" exemplified by Nyquist{\~O}s sampling criterion, which puts a disproportionate strain on current acquisition and processing systems as the size and desired resolution increases. In this paper, we address the "curse of dimensionality" by randomized dimensionality reduction of the FWI problem adapted from the field of CS. We invert for model updates by replacing the Gauss-Newton linearized subproblem for subsampled FWI with a sparsity promoting formulation, and solve this formulation using the SPGl1 algorithm. We speed up the algorithm and avoid overfitting the data by solving for the linearized updates only approximately. Our approach is successful because it reduces the size of seismic data volumes without loss of information. With this reduction, we can compute a Newton-like update with the reduced data volume at the cost of roughly one gradient update for the fully sampled wavefield.},
	keywords = {EAGE, Full-waveform inversion, Presentation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2011/li11EAGEfwirr/li11EAGEfwirr.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2011/li11EAGEfwirr/li11EAGEfwirr_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=50345},
	author = {Xiang Li and Aleksandr Y. Aravkin and Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {herrmann2011ICIAMconvexcompfwi,
	title = {FWI with sparse recovery: a convex-composite approach},
	booktitle = {ICIAM},
	year = {2011},
	month = {07},
	publisher = {ICIAM 2011},
	organization = {ICIAM 2011},
	abstract = {Iterative inversion algorithms require repeated simulation of 3D time-dependent acoustic, elastic, or electromagnetic wave fields, extending hundreds of wavelengths and hundreds of periods. Also, seismic data is rich in information at every representable scale. Thus simulation-driven optimization approaches to inversion impose great demands on simulator efficiency and accuracy. While computer hardware advances have been of critical importance in bringing inversion closer to practical application, algorithmic advances in simulator methodology have been equally important. Speakers in this two-part session will address a variety of numerical issues arising in the wave simulation, and in its application to inversion.},
	keywords = {Full-waveform inversion, ICIAM, Optimization},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICIAM/2011/herrmann2011ICIAMconvexcompfwi/herrmann2011ICIAMconvexcompfwi.pdf},
	author = {Felix J. Herrmann and Aleksandr Y. Aravkin and Tristan van Leeuwen and Xiang Li}
}
@conference {li2011SBGFmgnsu,
	title = {Modified Gauss-Newton with sparse updates},
	booktitle = {SBGF},
	year = {2011},
	publisher = {SBGF},
	organization = {SBGF},
	abstract = {Full-waveform inversion (FWI) is a data fitting procedure that relies on the collection of seismic data volumes and sophisticated computing to create high-resolution models.With the advent of FWI, the improvements in acquisition and inversion have been substantial, but these improvements come at a high cost because FWI involves extremely large multi-experiment data volumes. The main obstacle is the {\textquoteleft}curse of dimensionality{\textquoteright} exemplified by Nyquist{\textquoteright}s sampling criterion, which puts a disproportionate strain on current acquisition and processing systems as the size and desired resolution increases. In this paper, we address the {\textquoteleft}curse of dimensionality{\textquoteright} by using randomized dimensionality reduction of the FWI problem, coupled with a modified Gauss-Newton (GN) method designed to promote curvelet-domain sparsity of model updates. We solve for these updates using the spectral projected gradient method, implemented in the SPG1 software package. Our approach is successful because it reduces the size of seismic data volumes without loss of information. With this reduction, we can compute Gauss-Newton updates with the reduced data volume at the cost of roughly one gradient update for the fully sampled wavefield},
	keywords = {Full-waveform inversion, SBGF},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SBGF/2011/li11SBGFmgnsu/li11SBGFmgnsu.pdf},
	author = {Xiang Li and Felix J. Herrmann and Tristan van Leeuwen and Aleksandr Y. Aravkin}
}
@conference {herrmann2011SPIEmsp,
	title = {A modified, sparsity promoting, Gauss-Newton algorithm for seismic waveform inversion},
	booktitle = {Proc. SPIE},
	number = {81380V},
	year = {2011},
	month = {08},
	abstract = {Images obtained from seismic data are used by the oil and gas industry for geophysical exploration. Cutting-edge methods for transforming the data into interpretable images are moving away from linear approximations and high-frequency asymptotics towards Full Waveform Inversion (FWI), a nonlinear data-fitting procedure based on full data modeling using the wave-equation. The size of the problem, the nonlinearity of the forward model, and ill-posedness of the formulation all contribute to a pressing need for fast algorithms and novel regularization techniques to speed up and improve inversion results. In this paper, we design a modified Gauss-Newton algorithm to solve the PDE- constrained optimization problem using ideas from stochastic optimization and compressive sensing. More specifically, we replace the Gauss-Newton subproblems by randomly subsampled, -$\ell_1$ regularized subproblems. This allows us us significantly reduce the computational cost of calculating the updates and exploit the compressibility of wavefields in Curvelets. We explain the relationships and connections between the new method and stochastic optimization and compressive sensing (CS), and demonstrate the efficacy of the new method on a large-scale synthetic seismic example.},
	keywords = {Compressive Sensing, Full-waveform inversion, Optimization, SLIM},
	issn = {1},
	doi = {10.1117/12.893861},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SPIE/2011/herrmann2011SPIEmsp/herrmann2011SPIEmsp.pdf},
	author = {Felix J. Herrmann and Xiang Li and Aleksandr Y. Aravkin and Tristan van Leeuwen}
}
@conference {li2010SEGfwi,
	title = {Full-waveform inversion from compressively recovered model updates},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {29},
	year = {2010},
	month = {10},
	pages = {1029-1033},
	publisher = {SEG},
	organization = {SEG},
	abstract = {Full-waveform inversion relies on the collection of large multi-experiment data volumes in combination with a sophisticated back-end to create high-fidelity inversion results. While improvements in acquisition and inversion have been extremely successful, the current trend of incessantly pushing for higher quality models in increasingly complicated regions of the Earth reveals fundamental shortcomings in our ability to handle increasing problem size numerically. Two main culprits can be identified. First, there is the so-called {\textquoteleft}{\textquoteleft}curse of dimensionality{\textquoteright}{\textquoteright} exemplified by Nyquist{\textquoteright}s sampling criterion, which puts disproportionate strain on current acquisition and processing systems as the size and desired resolution increases. Secondly, there is the recent {\textquoteleft}{\textquoteleft}departure from Moore{\textquoteright}s law{\textquoteright}{\textquoteright} that forces us to lower our expectations to compute ourselves out of this. In this paper, we address this situation by randomized dimensionality reduction, which we adapt from the field of compressive sensing. In this approach, we combine deliberate randomized subsampling with structure-exploiting transform-domain sparsity promotion. Our approach is successful because it reduces the size of seismic data volumes without loss of information. With this reduction, we compute Newton-like updates at the cost of roughly one gradient update for the fully-sampled wavefield.},
	keywords = {Full-waveform inversion, Presentation, SEG},
	doi = {10.1190/1.3513022},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2010/li10SEGfwi/li10SEGfwi.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2010/li10SEGfwi/li10SEGfwi_pres.pdf},
	author = {Xiang Li and Felix J. Herrmann}
}
