@conference {tu2013SEGcle,
	title = {Controlling linearization errors in $\ell_1$ regularized inversion by rerandomization},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {32},
	year = {2013},
	month = {09},
	pages = {4640-4644},
	abstract = {Linearized inversion is a data fitting procedure that tries to match the observed seismic data with data predicted by linearized modelling. In practice, the observed data is not necessarily in the column space of the linearized modelling operator. This can be caused by lack of an accurate background velocity model or by coherent noises not explained by linearized modelling. Through carefully designed experiments, we ob- serve that a moderate data mismatch does not pose an issue if we can use all the data in the inversion. However, artifacts do arise from the mismatch when randomized dimensionality reduction techniques are adopted to speed up the inversion. To stabilize the inversion for dimensionality reduction with randomized source aggregates, we propose to rerandomize by drawing independent simultaneous sources occasionally during the inversion. The effect of this rerandomization is remarkable because it results in virtually artifact-free images at a cost comparable to a single reverse-time migration. Implications of our method are profound because we are now able to resolve fine-scale steep subsalt features in a computationally feasible manner.},
	keywords = {inversion, message passing, rerandomization, SEG, sparsity},
	doi = {10.1190/segam2013-1302.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/tu2013SEGcle/tu2013SEGcle.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/tu2013SEGcle/tu2013SEGcle_pres.pdf},
	author = {Ning Tu and Xiang Li and Felix J. Herrmann}
}
@presentation {tu2013SINBADrerand,
	title = {Controlling linearization errors with rerandomization},
	year = {2013},
	publisher = {SINBAD},
	abstract = {Least squares migration aims to fit the observed seismic data with data predicted by linearized modelling, by solving an PDE-constrained optimization problem. This problem is challenging mostly because of its prohibitive computational cost. To address the issue, dimensionality reduction techniques were proposed in the literature. However, the solution of the reduced problem can deviate from that of the full problem when there are components in the observed data that cannot be explained by linearized modelling. We solve the problem by rerandomizing our $\ell_1$ regularized inversion. In this presentation, I will explain the method and demonstrate what we can achieve with rerandomization, especially for resolving fine sub-salt structures.},
	keywords = {Presentation, SINBAD, SINBADSPRING2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Spring/tu2013SINBADrerand/tu2013SINBADrerand.pdf},
	author = {Ning Tu and Felix J. Herrmann}
}
