@presentation {vanleeuwen2013SINBADrpp,
	title = {Relaxing the physics: a penalty method for full-waveform inversion},
	year = {2013},
	publisher = {SINBAD},
	abstract = {Computationally efficient method of solving partial differential equation (PDE)-constrained optimization problems that occur in (geophysical) inversion problems. The method takes measured data from a physical system as input and minimizes an objective function that depends on an unknown model for the physical parameters, fields, and additional nuisance parameters such as the source function. The invention consists of a minimization procedure involving a cost functional comprising of a data-misfit term and a penalty term that measures how accurately the fields satisfy the PDE. The method is composed of two alternating steps, namely the solution of a system of equations forming the discretization of the data-augmented PDE, and the solution of physical model parameters from the PDE itself given the field that solves the data-augmented system and an estimate for the sources. Compared to all-at-once approaches to PDE-constrained optimization, there is no need to update and store the fields for all sources leading to significant memory savings. As in the all-at-once approach, the proposed method explores a larger search space and is therefore less sensitive to initial estimates for the physical model parameters. Contrary to the reduced formulation, the proposed method does not require the solution of an adjoint PDE, effectively halving the number of PDE solves and memory requirement. As in the reduced formulation, fields can be computed independently and aggregated, possibly in parallel.},
	keywords = {Presentation, SINBAD, SINBADFALL2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Fall/vanleeuwen2013SINBADrpp/vanleeuwen2013SINBADrpp.pdf},
	author = {Tristan van Leeuwen and Felix J. Herrmann}
}
@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 {aravkin2012ICASSProbustb,
	title = {Robust inversion via semistochastic dimensionality reduction},
	booktitle = {ICASSP},
	year = {2012},
	pages = {5245-5248},
	publisher = {ICASSP},
	organization = {ICASSP},
	abstract = {We consider a class of inverse problems where it is possible to aggregate the results of multiple experiments. This class includes problems where the forward model is the solution operator to linear ODEs or PDEs. The tremendous size of such problems motivates the use dimensionality reduction (DR) techniques based on randomly mixing experiments. These techniques break down, however, when robust data-fitting formulations are used, which are essential in cases of missing data, unusually large errors, and systematic features in the data unexplained by the forward model. We survey robust methods within a statistical framework, and propose a sampling optimization approach that allows DR. The efficacy of the methods are demonstrated for a large-scale seismic inverse problem using the robust Student{\textquoteright}s t-distribution, where a useful synthetic velocity model is recovered in the extreme scenario of 60\% corrupted data. The sampling approach achieves this recovery using 20\% of the effort required by a direct robust approach.},
	keywords = {ICASSP},
	doi = {10.1109/ICASSP.2012.6289103},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICASSP/2012/AravkinFriedlanderLeeuwen/AravkinFriedlanderLeeuwen.pdf},
	author = {Aleksandr Y. Aravkin and Michael P. Friedlander 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}
}
