@techreport {tschannen2014tdl,
	title = {Time domain least squares migration and dimensionality reduction},
	number = {TR-EOAS-2014-9},
	year = {2014},
	month = {06},
	institution = {UBC},
	abstract = {Least-squares seismic migration (LSM) is a wave equation based linearized inversion problem relying on the minimization of a least-squares misfit function, with respect to the medium perturbation, between recorded and modeled wavefields. Today{\textquoteright}s challenges in Hydrocarbon ex- ploration are to build high resolution images of more and more complicated geological reservoirs, which requires to handle very large systems of equations. The extreme size of the problem com- bined with the fact that it is ill-conditioned make LSM not yet feasible for industrial purposes. To overcome this "curse of dimensionality", dimension reduction and divide-and-conquer tech- niques that aim to decrease the computation time and the required memory, while conserving the image quality, have recently been developed. By borrowing ideas from stochastic optimiza- tion and compressive sensing, the imaging problem is reformulated as an L1-regularized, sparsity promoted LSM. The idea is to take advantage of the compressibility of the model perturbation in the curvelet domain and to work on series of smaller subproblems each involving a small ran- domized subset of data. We try two different subset sampling strategies, artificial randomized simultaneous sources experiments ("supershots") and drawing sequential shots firing at random source locations. These subsets are changed after each subproblem is solved. In both cases we obtain good migration results at significantly reduced computational cost. Application of these methods to a complicated synthetic model yields to encouraging results, underlining the usefulness of sparsity promotion and randomization in time stepping formulation.},
	keywords = {Compressive Sensing, sparsity promotion, Stochastic optimization, Wave equation migration},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2014/tschannen2014tdl/tschannen2014tdl.pdf},
	author = {Valentin Tschannen and Zhilong Fang and Felix J. Herrmann}
}
@article {mansour2012IEEETITrcs,
	title = {Recovering compressively sampled signals using partial support information},
	journal = {IEEE Transactions on Information Theory},
	volume = {58},
	number = {2},
	year = {2012},
	month = {02},
	pages = {1122-1134},
	publisher = {Department of Computer Science},
	address = {University of British Columbia, Vancouver},
	abstract = {We study recovery conditions of weighted $\ell_1$ minimization for signal reconstruction from compressed sensing measurements when partial support information is available. We show that if at least 50\% of the (partial) support information is accurate, then weighted $\ell_1$ minimization is stable and robust under weaker sufficient conditions than the analogous conditions for standard $\ell_1$ minimization. Moreover, weighted $\ell_1$ minimization provides better upper bounds on the reconstruction error in terms of the measurement noise and the compressibility of the signal to be recovered. We illustrate our results with extensive numerical experiments on synthetic data and real audio and video signals.},
	keywords = {Compressive Sensing},
	doi = {10.1109/TIT.2011.2167214},
	url = {https://slim.gatech.edu/Publications/Public/Journals/IEEETransInformationTheory/2012/mansour2012IEEETITrcs/mansour2012IEEETITrcs.pdf},
	author = {Michael P. Friedlander and Hassan Mansour and Rayan Saab and Ozgur Yilmaz}
}
