@conference {peters2014EAGEweb,
	title = {Wave-equation based inversion with the penalty method: adjoint-state versus wavefield-reconstruction inversion},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2014},
	month = {06},
	abstract = {In this paper we make a comparison between wave-equation based inversions based on the adjoint-state and penalty methods. While the adjoint-state method involves the minimization of a data-misfit and exact solutions of the wave-equation for the current velocity model, the penalty-method aims to first find a wavefield that jointly fits the data and honours the physics, in a least-squares sense. Given this reconstructed wavefield, which is a proxy for the true wavefield in the true model, we calculate updates for the velocity model. Aside from being less nonlinear{\textendash}the acoustic wave equation is linear in the wavefield and model parameters but not in both{\textendash}the inversion is carried out over a solution space that includes both the model and the wavefield. This larger search space allows the algortihm to circumnavigate local minima, very much in the same way as recently proposed model extentions try to acomplish. We include examples for low frequencies, where we compare full-waveform inversion results for both methods, for good and bad starting models, and for high frequencies where we compare reverse-time migration with linearized imaging based on wavefield-reconstruction inversion. The examples confirm the expected benefits of the proposed method.},
	keywords = {EAGE, Full-waveform inversion, Imaging, Optimization, penalty method},
	doi = {10.3997/2214-4609.20140704},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/peters2014EAGEweb/peters2014EAGEweb.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/peters2014EAGEweb/peters2014EAGEweb_pres.pdf},
	author = {Bas Peters and Felix J. Herrmann and Tristan van Leeuwen}
}
@conference {tu2013EAGElsm,
	title = {Fast least-squares migration with multiples and source estimation},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2013},
	month = {06},
	abstract = {The advent of modern computing has made it possible to do seismic imaging using least-squares reverse-time migration. We obtain superior images by solving an optimization problem that recovers the true-amplitude images. However, its success hinges on overcoming several issues, including overwhelming problem size, unknown source wavelet, and interfering coherent events like multiples. In this abstract, we reduce the problem size by using ideas from compressive sensing, and estimate source wavelet by generalized variable projection. We also demonstrate how to invert for subsurface information encoded in surface-related multiples by incorporating the free-surface operator as an areal source in reverse-time migration. Our synthetic examples show that multiples help to improve the resolution of the image, as well as remove the amplitude ambiguity in wavelet estimation.},
	keywords = {EAGE, Imaging, multiples, source estimation, sparse},
	doi = {10.3997/2214-4609.20130727},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2013/tu2013EAGElsm/tu2013EAGElsm.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2013/tu2013EAGElsm/tu2013EAGElsm_pres.pdf},
	author = {Ning Tu and Aleksandr Y. Aravkin and Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {aravkin2013ICASSPssi,
	title = {Sparse seismic imaging using variable projection},
	booktitle = {ICASSP},
	year = {2013},
	month = {05},
	abstract = {We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how this data was generated. For example, a sparse green{\textquoteright}s function may be recovered from seismic experimental data using sparsity optimization when the source signature is known. Unfortunately, in practice this information is often missing, and must be recovered from data along with the signal using deconvolution techniques. In this paper, we present a novel methodology to simulta- neously solve for the sparse signal and auxiliary parameters using a recently proposed variable projection technique. Our main contribution is to combine variable projection with spar- sity promoting optimization, obtaining an efficient algorithm for large-scale sparse deconvolution problems. We demon- strate the algorithm on a seismic imaging example.},
	keywords = {Imaging, Optimization, sparsity, variable projection},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICASSP/2013/aravkin2013ICASSPssi/aravkin2013ICASSPssi.pdf},
	author = {Aleksandr Y. Aravkin and Tristan van Leeuwen and Ning Tu}
}
@techreport {vanleeuwen2012SEGparallel,
	title = {A parallel, object-oriented framework for frequency-domain wavefield imaging and inversion.},
	number = {TR-EOAS-2012-2},
	year = {2012},
	month = {04},
	institution = {Department of Earth and Ocean Sciences},
	address = {University of British Columbia, Vancouver},
	abstract = {We present a parallel object-oriented matrix-free framework for frequency-domain seismic modeling, imaging and inversion. The key aspects of the framework are its modularity and level of abstraction, which allows us to write code that reflects the underlying mathematical structure and develop unit-tests that guarantee the fidelity of the code. By overloading standard linear-algebra operations, such as matrix-vector multiplications, we can use standard optimization packages to work with our code without any modification. This leads to a scalable testbed on which new methods can be rapidly prototyped and tested on medium-sized 2D problems. Although our current implementation uses (parallel) Matlab, all of these design principles can also be met by using lower-level languages which is important when we want to scale to realistic 3D problems. We present some numerical examples on synthetic data.},
	keywords = {Imaging, inversion, Modeling, SEG},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2012/vanleeuwen2012SEGparallel/vanleeuwen2012SEGparallel.pdf},
	author = {Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {vanleeuwen2011ICIAMcbmcwe,
	title = {A correlation-based misfit criterion for wave-equation traveltime tomography},
	booktitle = {ICIAM},
	year = {2011},
	note = {Presented at ICIAM 2011, Vancouver BC},
	month = {07},
	publisher = {ICIAM 2011},
	organization = {ICIAM 2011},
	abstract = {The inference of subsurface medium parameters from seismic data can be posed as a PDE-constrained data-fitting procedure. This approach is successful in reconstructing medium perturbations that are in the order of the wavelength. In practice, the data lack low frequency content and this means that one needs a good initial guess of the slowly varying component of the medium. For a wrong starting model an iterative reconstruction procedure is likely to end up in a local minimum. We propose to use a different measure of the misfit that makes the optimization problem well-posed in terms of the slowly varying velocity structures. This procedure can be seen as a generalization of ray-based traveltime tomography. We discuss the theoretical underpinnings of the method and give some numerical examples.},
	keywords = {ICIAM, Imaging, Presentation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICIAM/2011/vanleeuwen2011ICIAMcbmcwe/vanleeuwen2011ICIAMcbmcwe.pdf},
	author = {Tristan van Leeuwen}
}
@conference {vanleeuwen2011SEGext,
	title = {Probing the extended image volume},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {30},
	year = {2011},
	month = {09},
	pages = {4045-4050},
	publisher = {SEG},
	organization = {SEG},
	abstract = {The prestack image volume can be defined as a cross- correlation of the source and receivers wavefields for non-zero space and time lags. If the background velocity is kinemati- cally acceptable, this image volume will have its main contributions at zero lag, even for complex models. Thus, it is an ideal tool for wave-equation migration velocity analysis in the presence of strong lateral heterogeneity. In particular, it allows us to pose migration velocity analysis as a PDE-constrained optimization problem, where the goal is to minimize the energy in the image volume at non-zero lag subject to fitting the data approximately. However, it is computationally infeasi- ble to explicitly form the whole image volume. In this paper, we discuss several ways to reduce the computational costs involved in computing the image volume and evaluating the focusing criterion. We reduce the costs for calculating the data by randomized source synthesis. We also present an efficient way to subsample the image volume. Finally, we propose an alternative optimization criterion and suggest a multiscale inversion strategy for wave-equation MVA.},
	keywords = {Imaging, SEG},
	doi = {10.1190/1.3628051},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2011/vanleeuwen11SEGext/vanleeuwen11SEGext.pdf},
	author = {Tristan van Leeuwen and Felix J. Herrmann}
}
