@article {esser2016tvr,
	title = {Total-variation regularization strategies in full-waveform inversion},
	journal = {SIAM Journal on Imaging Sciences},
	volume = {11},
	number = {1},
	year = {2018},
	note = {(SIAM Journal on Imaging Sciences)},
	pages = {376-406},
	abstract = {We propose an extended full-waveform inversion formulation that includes general convex constraints on the model. Though the full problem is highly nonconvex, the overarching optimization scheme arrives at geologically plausible results by solving a sequence of relaxed and warm-started constrained convex subproblems. The combination of box, total-variation, and successively relaxed asymmetric total-variation constraints allows us to steer free from parasitic local minima while keeping the estimated physical parameters laterally continuous and in a physically realistic range. For accurate starting models, numerical experiments carried out on the challenging 2004 BP velocity benchmark demonstrate that bound and total-variation constraints improve the inversion result significantly by removing inversion artifacts, related to source encoding, and by clearly improved delineation of top, bottom, and flanks of a high-velocity high-contrast salt inclusion. The experiments also show that for poor starting models these two constraints by themselves are insufficient to detect the bottom of high-velocity inclusions such as salt. Inclusion of the one-sided asymmetric total-variation constraint overcomes this issue by discouraging velocity lows to buildup during the early stages of the inversion. To the author{\textquoteright}s knowledge the presented algorithm is the first to successfully remove the imprint of local minima caused by poor starting models and band-width limited finite aperture data.},
	keywords = {constrained optimization, Full-waveform inversion, hinge loss, salt, total variation},
	doi = {10.1137/17M111328X},
	url = {https://slim.gatech.edu/Publications/Public/Journals/SIAMJournalOnImagingSciences/2018/esser2016tvr/esser2016tvr.pdf},
	url2 = {https://doi.org/10.1137/17M111328X},
	author = {Ernie Esser and Llu{\'\i}s Guasch and Tristan van Leeuwen and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@article {peters2016cvp,
	title = {Constraints versus penalties for edge-preserving full-waveform inversion},
	journal = {The Leading Edge},
	volume = {36},
	number = {1},
	year = {2017},
	note = {(The Leading Edge)},
	month = {01},
	pages = {94-100},
	abstract = {Full-waveform inversion is challenging in complex geologic areas. Even when provided with an accurate starting model, the inversion algorithms often struggle to update the velocity model. Compared with other areas in applied geophysics, including prior information in full-waveform inversion is still in its relative infancy. In part, this is due to the fact that it is difficult to incorporate prior information that relates to geologic settings where strong discontinuities in the velocity model dominate, because these settings call for nonsmooth regularizations. We tackle this problem by including constraints on the spatial variations and value ranges of the inverted velocities, as opposed to adding penalties to the objective, which is more customary in mainstream geophysical inversion. By demonstrating the lack of predictability of edge-preserving inversion when the regularization is in the form of an added penalty term, we advocate the inclusion of constraints instead. Our examples show that the latter leads to more predictable results and to significant improvements in the delineation of salt bodies when these constraints are relaxed gradually in combination with extending the search space to approximately fit the observed data but not the noise.},
	keywords = {algorithm, full waveform inversion, noise, Optimization, penalty methods, salt dome, total variation},
	doi = {10.1190/tle36010094.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2016/peters2016cvp/peters2016cvp.html},
	author = {Bas Peters and Felix J. Herrmann}
}
