@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}
}
@presentation {wang2017SINBADFnra,
	title = {Noise robust and time-domain formulations of Wavefield Reconstruction Inversion},
	year = {2017},
	publisher = {SINBAD},
	abstract = {We propose a wave-equation-based subsurface inversion method that in many cases is more robust than conventional Full-Waveform Inversion. The new formulation is written in a denoising form that allows the synthetic data to match the observed ones up to a small error. Compared to regular Full-Waveform Inversion, our method treats the noise arising from the data meassuring/recording process and that from the synthetic modelling process separately. Compared to Wavefields Reconstruction Inversion, the new formulation mitigates the difficulty of choosing the penalty parameter λ. To solve the proposed optimization problem, we develop an efficient frequency domain algorithm that alternatively updates the model and the data. Numerical experiments confirm strong stability of the proposed method by comparisons between the results of our algorithm with that from both plain FWI and a weighted formulation of the FWI. We also discuss a new memory efficient time-domain formulation for Wavefield Reconstruction Inversion based on duality.},
	keywords = {Presentation, SINBAD, SINBADFALL2017, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/wang2017SINBADFnra/wang2017SINBADFnra.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/wang2017SINBADFnra/wang2017SINBADFnra.mov},
	author = {Rongrong Wang and Mathias Louboutin and Bas Peters and Emmanouil Daskalakis 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}
}
@presentation {wang2013SINBADnru,
	title = {Noise reduction by using interferometric measurements},
	year = {2013},
	publisher = {SINBAD},
	abstract = {The interferometric formulation of linear wave-based inversion problem was proposed by Demanet and Jugnon recently. Instead of directly fitting the data, they proposed to fit a subset of the data{\textquoteright}s cross-correlation. It can be verified that if the full cross-correlation is used, then the problem is equivalent to the usual least square problem. The subsampling, which is usually considered to cause instability to the solution, is surprisingly useful in this setting. Numerical experiments for the inverse source problem and the inverse scatting problem have both suggested that a {\textquoteright}good{\textquoteright} sampling strategy can actually increase the stability under modeling error caused by the uncertainty of a kinetic nature. We will study the mathematical mechanism behind this phenomenon, and try to see whether or not there exists a universally {\textquoteright}good{\textquoteright} sampling strategy independent of the types of forward operators we use.},
	keywords = {Presentation, SINBAD, SINBADFALL2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Fall/wang2013SINBADnru/wang2013SINBADnru.pdf},
	author = {Rongrong Wang and Bas Peters and Felix J. Herrmann}
}
