@article {vanleeuwen2015IPpmp,
	title = {A penalty method for PDE-constrained optimization in inverse problems},
	journal = {Inverse Problems},
	volume = {32},
	number = {1},
	year = {2015},
	note = {(Inverse Problems)},
	month = {12},
	pages = {015007},
	abstract = {Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for several right-hand sides. Such PDE-constrained problems can be solved by finding a stationary point of the Lagrangian, which entails simultaneously updating the parameters and the (adjoint) state variables. For large-scale problems, such an all-at-once approach is not feasible as it requires storing all the state variables. In this case one usually resorts to a reduced approach where the constraints are explicitly eliminated (at each iteration) by solving the PDEs. These two approaches, and variations thereof, are the main workhorses for solving PDE-constrained optimization problems arising from inverse problems. In this paper, we present an alternative method that aims to combine the advantages of both approaches. Our method is based on a quadratic penalty formulation of the constrained optimization problem. By eliminating the state variable, we develop an efficient algorithm that has roughly the same computational complexity as the conventional reduced approach while exploiting a larger search space. Numerical results show that this method indeed reduces some of the nonlinearity of the problem and is less sensitive to the initial iterate.},
	keywords = {Inverse problems, Optimization, PDE, penalty method},
	url = {https://slim.gatech.edu/Publications/Public/Journals/InverseProblems/2015/vanleeuwen2015IPpmp/vanleeuwen2015IPpmp.pdf},
	url2 = {http://stacks.iop.org/0266-5611/32/i=1/a=015007},
	author = {Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {leeuwen2014EAGEntf,
	title = {A new take on FWI: wavefield reconstruction inversion},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2014},
	month = {06},
	abstract = {We discuss a recently proposed novel method for waveform inversion: Wavefield Reconstruction Inversion (WRI). As opposed to conventional FWI {\textendash} which attempts to minimize the error between observed and predicted data obtained by solving a wave equation {\textendash} WRI reconstructs a wave-field from the data and extracts a model-update from this wavefield by minimizing the wave-equation residual. The method does not require explicit computation of an adjoint wavefield as all the necessary information is contained in the reconstructed wavefield. We show how the corresponding model updates can be interpreted physically analogously to the conventional imaging-condition-based approach.},
	keywords = {EAGE, Full-waveform inversion, Optimization, penalty method, Wavefield Reconstruction Inversion},
	doi = {10.3997/2214-4609.20140703},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/leeuwen2014EAGEntf/leeuwen2014EAGEntf.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/leeuwen2014EAGEntf/leeuwen2014EAGEntf_pres.pdf},
	author = {Tristan van Leeuwen and Felix J. Herrmann and Bas Peters}
}
@techreport {herrmann2014pmpde,
	title = {A penalty method for PDE-constrained optimization},
	number = {WO 2014/172787},
	year = {2014},
	note = {(International publication date 30 October 2014. International publication number WO 2014/172787.)},
	month = {10},
	institution = {UBC},
	type = {Patent},
	abstract = {The invention is directed to a computer-implemented method for obtaining a physical model having physical model parameters wherein solutions to one or more partial-differential-equations (PDE{\textquoteright}s) are calculated ans wherein (i) an appropriate initial model is selected, (ii) setup a system of equations referred to as the data-augmented PDE for the field, comprising of the discretized PDE, the sampling operator, the source function and the observed data, and solve the data-augmented PDE in a suitable manner to obtain a field that both satisfies the PDE and fits the data to some degree, (iii) setup a system of equations by using the PDE, the source function and the field obtained in step (ii) and solve this system of equations in a suitable manner to obtain an update of the physical model parameters and repeat steps (ii)-(iii) until a predetermined stopping criterion is met.},
	keywords = {Optimization, patent, penalty method},
	url = {https://slim.gatech.edu/Publications/Public/Patents/2014/herrmann2014pmpde/herrmann2014pmpde_WO2014172787.pdf},
	url2 = {http://patentscope.wipo.int/search/en/WO2014172787},
	author = {Felix J. Herrmann and Tristan van Leeuwen}
}
@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}
}
@article {VanLeeuwen11TRfwiwse,
	title = {Fast waveform inversion without source encoding},
	journal = {Geophysical Prospecting},
	volume = {61},
	year = {2013},
	note = {Article first published online: 10 JULY 2012},
	month = {06},
	pages = {10-19},
	abstract = {Randomized source encoding has recently been proposed as a way to dramatically reduce the costs of full waveform inversion. The main idea is to replace all sequential sources by a small number of simultaneous sources. This introduces random crosstalk in the model updates and special stochastic optimization strategies are required to deal with this. Two problems arise with this approach: i) source encoding can only be applied to fixed-spread acquisition setups, and ii) stochastic optimization methods tend to converge very slowly, relying on averaging to get rid of the cross-talk. Although the slow convergence is partly offset by the low iteration cost, we show that conventional optimization strategies are bound to outperform stochastic methods in the long run. In this paper we argue that we don{\textlnot}{\o}t need randomized source encoding to reap the benefits of stochastic optimization and we review an optimization strategy that combines the benefits of both conventional and stochastic optimization. The method uses a gradually increasing batch of sources. Thus, iterations are very cheap initially and this allows the method to make fast progress in the beginning. As the batch size grows, the method behaves like conventional optimization, allowing for fast convergence. Numerical examples suggest that the stochastic and hybrid method perform equally well with and without source encoding and that the hybrid method outperforms both conventional and stochastic optimization. The method does not rely on source encoding techniques and can thus be applied to non fixed-spread data.},
	keywords = {FWI, Optimization, SLIM},
	doi = {10.1111/j.1365-2478.2012.01096.x},
	url = {http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2478.2012.01096.x/abstract},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalProspecting/2013/VanLeeuwen11TRfwiwse/VanLeeuwen11TRfwiwse.pdf},
	author = {Tristan van Leeuwen and Felix J. Herrmann}
}
@article {herrmann2013TLEffwi,
	title = {Frugal full-waveform inversion: from theory to a practical algorithm},
	journal = {The Leading Edge},
	volume = {32},
	number = {9},
	year = {2013},
	month = {09},
	pages = {1082-1092},
	abstract = {As conventional oil and gas fields are maturing, our profession is challenged to come up with the next-generation of more and more sophisticated exploration tools. In exploration seismology this trend has led to the emergence of wave-equation based inversion technologies such as reverse-time migration and full-waveform inversion. While significant progress has been made in wave-equation based inversion, major challenges remain in the development of robust and computationally feasible workflows that give reliable results in geophysically challenging areas that may include ultra-low shear velocity zones or high-velocity salt. Moreover, sub-salt production carries risks that needs mitigation, which raises the bar from creating sub-salt images to inverting for sub-salt overpressure.},
	keywords = {Optimization, waveform inversion},
	doi = {10.1190/tle32091082.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2013/herrmann2013ffwi/herrmann2013ffwi.html},
	author = {Felix J. Herrmann and Andrew J. Calvert and Ian Hanlon and Mostafa Javanmehri and Rajiv Kumar and Tristan van Leeuwen and Xiang Li and Brendan R. Smithyman and Eric Takam Takougang and Haneet Wason}
}
@techreport {vanLeeuwen2013Penalty2,
	title = {A penalty method for PDE-constrained optimization},
	number = {TR-EOAS-2013-6},
	year = {2013},
	month = {04},
	institution = {UBC},
	abstract = {We present a method for solving PDE constrained optimization problems based on a penalty formulation. This method aims to combine advantages of both full-space and reduced methods by exploiting a large search-space (consisting of both control and state variables) while allowing for an efficient implementation that avoids storing and updating the state-variables. This leads to a method that has roughly the same per-iteration complexity as conventional reduced approaches while dening an objective that is less non-linear in the control variable by implicitly relaxing the constraint. We apply the method to a seismic inverse problem where it leads to a particularly ecient implementation when compared to a conventional reduced approach as it avoids the use of adjoint state-variables. Numerical examples illustrate the approach and suggest that the proposed formulation can indeed mitigate some of the well-known problems with local minima in the seismic inverse problem.},
	keywords = {Optimization, waveform inversion},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2013/vanLeeuwen2013Penalty2/vanLeeuwen2013Penalty2.pdf},
	author = {Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {herrmann2013SEGpmc,
	title = {A penalty method for PDE-constrained optimization with applications to wave-equation based seismic inversion},
	booktitle = {SEG Workshop on Computational Mathematics for Geophysics; Houston},
	year = {2013},
	month = {09},
	keywords = {Optimization, penalty method, SEG, workshop},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/herrmann2013SEGpmc/herrmann2013SEGpmc_pres.pdf},
	author = {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}
}
@article {Li11TRfrfwi,
	title = {Fast randomized full-waveform inversion with compressive sensing},
	journal = {Geophysics},
	volume = {77},
	number = {3},
	year = {2012},
	month = {05},
	pages = {A13-A17},
	abstract = {Wave-equation based seismic inversion can be formulated as a nonlinear inverse problem where the medium properties are obtained via minimization of a least- squares misfit functional. The demand for higher resolution models in more geologically complex areas drives the need to develop techniques that explore the special structure of full-waveform inversion to reduce the computational burden and to regularize the inverse problem. We meet these goals by using ideas from compressive sensing and stochastic optimization to design a novel Gauss-Newton method, where the updates are computed from random subsets of the data via curvelet-domain sparsity promotion. Application of this idea to a realistic synthetic shows improved results compared to quasi-Newton methods, which require passes through all data. Two different subset sampling strategies are considered: randomized source encoding, and drawing sequential shots firing at random source locations from marine data with missing near and far offsets. In both cases, we obtain excellent inversion results compared to conventional methods at reduced computational costs.},
	keywords = {Compressive Sensing, FWI, Optimization, SLIM},
	doi = {10.1190/geo2011-0410.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2012/Li11TRfrfwi/Li11TRfrfwi.pdf},
	author = {Xiang Li and Aleksandr Y. Aravkin and Tristan van Leeuwen and Felix J. Herrmann}
}
@techreport {vanleeuwen2012smii,
	title = {A parallel matrix-free framework for frequency-domain seismic modelling, imaging and inversion in Matlab},
	number = {TR-EOAS-2012-5},
	year = {2012},
	month = {07},
	abstract = {I present a parallel matrix-free framework for frequency-domain seismic modeling, imaging and inversion. The framework provides basic building blocks for designing and testing optimization-based formulations of both linear and non-linear seismic in- verse problems. By overloading standard linear-algebra operations, such as matrix-vector multiplications, standard optimization packages can be used to work with the 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. I present some numerical examples on both linear and non-linear seismic inverse problems.},
	keywords = {Matlab, object-oriented programming, Optimization, seismic imaging},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2012/vanleeuwen2012smii/vanleeuwen2012smii.pdf},
	author = {Tristan van Leeuwen}
}
@article {Aravkin11TRridr,
	title = {Robust inversion, dimensionality reduction, and randomized sampling},
	journal = {Mathematical Programming},
	volume = {134},
	number = {1},
	year = {2012},
	month = {08},
	pages = {101-125},
	abstract = {We consider a class of inverse problems in which the forward model is the solution operator to linear ODEs or PDEs. This class admits several dimensionality-reduction techniques based on data averaging or sampling, which are especially useful for large-scale problems. We survey these approaches and their connection to stochastic optimization. The data-averaging approach is only viable, however, for a least-squares misfit, which is sensitive to outliers in the data and artifacts unexplained by the forward model. This motivates us to propose a robust formulation based on the Student{\textquoteright}s t-distribution of the error. We demonstrate how the corresponding penalty function, together with the sampling approach, can obtain good results for a large-scale seismic inverse problem with 50 \% corrupted data.},
	keywords = {FWI, Inverse problems, Optimization, Robust estimation, Seismic inversion, Stochastic optimization},
	doi = {10.1007/s10107-012-0571-6},
	url = {http://www.springerlink.com/content/35rwr101h5736340/},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/MathematicalProgramming/aravkin2012MPrid/aravkin2012MPrid.pdf},
	author = {Aleksandr Y. Aravkin and Michael P. Friedlander and Felix J. Herrmann and Tristan van Leeuwen}
}
@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 {vanleeuwen2011EAGEhsdomwi,
	title = {A hybrid stochastic-deterministic optimization method for waveform inversion},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2011},
	month = {05},
	abstract = {Present-day high quality 3D acquisition can give us lower frequencies and longer offsets with which to invert. However, the computational costs involved in handling this data explosion are tremendous. Therefore, recent developments in full-waveform inversion have been geared towards reducing the computational costs involved. A key aspect of several approaches that have been proposed is a dramatic reduction in the number of sources used in each iteration. A reduction in the number of sources directly translates to less PDE-solves and hence a lower computational cost. Recent attention has been drawn towards reducing the sources by randomly combining the sources in to a few supershots, but other strategies are also possible. In all cases, the full data misfit, which involves all the sequential sources, is replaced by a reduced misfit that is much cheaper to evaluate because it involves only a small number of sources (batchsize). The batchsize controls the accuracy with which the reduced misfit approximates the full misfit. The optimization of such an inaccurate, or noisy, misfit is the topic of stochastic optimization. In this paper, we propose an optimization strategy that borrows ideas from the field of stochastic optimization. The main idea is that in the early stage of the optimization, far from the true model, we do not need a very accurate misfit. The strategy consists of gradually increasing the batchsize as the iterations proceed. We test the proposed strategy on a synthetic dataset. We achieve a very reasonable inversion result at the cost of roughly 13 evaluations of the full misfit. We observe a speed-up of roughly a factor 20.},
	keywords = {EAGE, Full-waveform inversion, Optimization, Presentation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2011/vanleeuwen11EAGEhsdomwi/vanleeuwen11EAGEhsdomwi.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2011/vanleeuwen11EAGEhsdomwi/vanleeuwen11EAGEhsdomwi_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=50341},
	author = {Tristan van Leeuwen and Felix J. Herrmann and Mark Schmidt and Michael P. Friedlander}
}
@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 {aravkin2011EAGEnspf,
	title = {A nonlinear sparsity promoting formulation and algorithm for full waveform inversion},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2011},
	month = {05},
	abstract = {Full Waveform Inversion (FWI) is a computational procedure to extract medium parameters from seismic data. FWI is typically formulated as a nonlinear least squares optimization problem, and various regularization techniques are used to guide the optimization because the problem is illposed. In this paper, we propose a novel sparse regularization which exploits the ability of curvelets to efficiently represent geophysical images. We then formulate a corresponding sparsity promoting constrained optimization problem, which we call Nonlinear Basis Pursuit Denoise (NBPDN) and present an algorithm to solve this problem to recover medium parameters. The utility of the NBPDN formulation and efficacy of the algorithm are demonstrated on a stylized cross-well experiment, where a sparse velocity perturbation is recovered with higher quality than the standard FWI formulation (solved with LBFGS). The NBPDN formulation and algorithm can recover the sparse perturbation even when the data volume is compressed to 5 \% of the original size using random superposition.},
	keywords = {EAGE, Full-waveform inversion, Optimization},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2011/aravkin11EAGEnspf/aravkin11EAGEnspf.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2011/aravkin11EAGEnspf/aravkin11EAGEnspf_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=50199},
	author = {Aleksandr Y. Aravkin and James V. Burke and Felix J. Herrmann and Tristan van Leeuwen}
}
@conference {aravkin2011SEGrobust,
	title = {Robust full-waveform inversion using the Student{\textquoteright}s t-distribution},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {30},
	year = {2011},
	month = {09},
	pages = {2669-2673},
	publisher = {SEG},
	organization = {SEG},
	abstract = {Full-waveform inversion (FWI) is a computational procedure to extract medium parameters from seismic data. Robust methods for FWI are needed to overcome sensitivity to noise and in cases where modeling is particularly poor or far from the real data generating process. We survey previous robust methods from a statistical perspective, and use this perspective to derive a new robust method by assuming the random errors in our model arise from the Student{\textquoteright}s t-distribution. We show that in contrast to previous robust methods, the new method progres- sively down-weighs large outliers, effectively ignoring them once they are large enough. This suggests that the new method is more robust and suitable for situations with very poor data quality or modeling. Experiments show that the new method recovers as well or better than previous robust methods, and can recover models with quality comparable to standard methods on noise-free data when some of the data is completely corrupted, and even when a marine acquisition mask is entirely ignored in the modeling. The ability to ignore a marine acquisition mask via robust FWI methods offers an opportunity for stochastic optimization methods in marine acquisition.},
	keywords = {Full-waveform inversion, Optimization, SEG},
	doi = {10.1190/1.3627747},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2011/aravkin11SEGrobust/aravkin11SEGrobust.pdf},
	author = {Aleksandr Y. Aravkin and Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {aravkin2011ICIAMrfwiu,
	title = {Robust FWI using Student{\textquoteright}s t-distribution},
	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, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICIAM/2011/aravkin2011ICIAMrfwiu/aravkin2011ICIAMrfwiu.pdf},
	author = {Aleksandr Y. Aravkin and Tristan van Leeuwen and Felix J. Herrmann}
}
@article {vanLeeuwen2010IJGswi,
	title = {Seismic waveform inversion by stochastic optimization},
	journal = {International Journal of Geophysics},
	volume = {2011},
	year = {2011},
	note = {Article ID: 689041, 18pages},
	month = {12},
	abstract = {We explore the use of stochastic optimization methods for seismic waveform inversion. The basic principle of such methods is to randomly draw a batch of realizations of a given misfit function and goes back to the 1950s. The ultimate goal of such an approach is to dramatically reduce the computational cost involved in evaluating the misfit. Following earlier work, we introduce the stochasticity in waveform inversion problem in a rigorous way via a technique called randomized trace estimation. We then review theoretical results that underlie recent developments in the use of stochastic methods for waveform inversion. We present numerical experiments to illustrate the behavior of different types of stochastic optimization methods and investigate the sensitivity to the batch size and the noise level in the data. We find that it is possible to reproduce results that are qualitatively similar to the solution of the full problem with modest batch sizes, even on noisy data. Each iteration of the corresponding stochastic methods requires an order of magnitude fewer PDE solves than a comparable deterministic method applied to the full problem, which may lead to an order of magnitude speedup for waveform inversion in practice.},
	keywords = {FWI, Optimization, SLIM},
	doi = {10.1155/2011/689041},
	url = {https://slim.gatech.edu/Publications/Public/Journals/InternationJournalOfGeophysics/2011/vanLeeuwen10IJGswi/vanLeeuwen10IJGswi.pdf},
	author = {Tristan van Leeuwen and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@conference {aravkin2011ICIAMspf,
	title = {Sparsity promoting formulations and algorithms for FWI},
	booktitle = {ICIAM},
	year = {2011},
	note = {Presented at AMP Medical and Seismic Imaging, 2011, Vancouver BC.},
	month = {07},
	publisher = {ICIAM 2011},
	organization = {ICIAM 2011},
	abstract = {Full Waveform Inversion (FWI) is a computational procedure to extract medium parameters from seismic data. FWI is typically formulated as a nonlinear least squares optimization problem, and various regularization techniques are used to guide the optimization because the problem is ill-posed. We propose a novel sparse regularization which exploits the ability of curvelets to efficiently represent geophysical images. We then formulate a corresponding sparsity promoting constrained optimization problem, which we solve using an open source algorithm. The techniques are applicable to any inverse problem where sparsity modeling is appropriate. We demonstrate the efficacy of the formulation on a toy example (stylized cross-well experiment) and on a realistic Seismic example (partial Marmoussi model). We also discuss the tradeoff between model fit and sparsity promotion, with a view to extend existing techniques for linear inverse problems to the case where the forward model is nonlinear.},
	keywords = {Full-waveform inversion, Optimization, Presentation, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICIAM/2011/aravkin2011ICIAMspf/aravkin2011ICIAMspf_pres.pdf},
	author = {Aleksandr Y. Aravkin and Tristan van Leeuwen and James V. Burke and Felix J. Herrmann}
}
