@conference {dasilva2013SAMPTAhtuck,
	title = {Hierarchical Tucker tensor optimization - applications to tensor completion},
	year = {2013},
	month = {07},
	abstract = {In this work, we develop an optimization framework for problems whose solutions are well-approximated by Hierarchical Tucker tensors, an efficient structured tensor format based on recursive subspace factorizations. Using the differential geometric tools presented here, we construct standard optimization algorithms such as Steepest Descent and Conjugate Gradient, for interpolating tensors in HT format. We also empirically examine the importance of one{\textquoteright}s choice of data organization in the success of tensor recovery by drawing upon insights from the Matrix Completion literature. Using these algorithms, we recover various seismic data sets with randomly missing source pairs.},
	keywords = {differential geometry, hierarchical tucker, riemannian optimization, SAMPTA, structured tensor, tensor interpolation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SAMPTA/2013/dasilva2013SAMPTAhtuck/dasilva2013SAMPTAhtuck.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SAMPTA/2013/dasilva2013SAMPTAhtuck/dasilva2013SAMPTAhtuck_pres.pdf},
	author = {Curt Da Silva and Felix J. Herrmann}
}
@conference {herrmann2009SAMPTAcws,
	title = {Compressive-wavefield simulations},
	booktitle = {SAMPTA},
	year = {2009},
	publisher = {SAMPTA},
	organization = {SAMPTA},
	abstract = {Full-waveform inversion{\textquoteright}s high demand on computational resources forms, along with the non-uniqueness problem, the major impediment withstanding its widespread use on industrial-size datasets. Turning modeling and inversion into a compressive sensing problem{\textendash}-where simulated data are recovered from a relatively small number of independent simultaneous sources{\textendash}-can effectively mitigate this high-cost impediment. The key is in showing that we can design a sub-sampling operator that commutes with the time-harmonic Helmholtz system. As in compressive sensing, this leads to a reduction in simulation cost. Moreover, this reduction is commensurate with the transform-domain sparsity of the solution, implying that computational costs are no longer determined by the size of the discretization but by transform-domain sparsity of the solution of the CS problem which forms our data. The combination of this sub-sampling strategy with our recent work on implicit solvers for the Helmholtz equation provides a viable alternative to full-waveform inversion schemes based on explicit finite-difference methods.},
	keywords = {SAMPTA},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SAMPTA/2009/Herrmann09SAMPTAcws/Herrmann09SAMPTAcws.pdf},
	author = {Felix J. Herrmann and Yogi A. Erlangga and Tim T.Y. Lin}
}
