@article {liu2018ssi,
	title = {Simultaneous-shot inversion for PDE-constrained optimization problems with missing data},
	journal = {Inverse Problems},
	volume = {35},
	number = {2},
	year = {2018},
	note = {(Inverse Problems)},
	pages = {025003},
	abstract = {Stochastic optimization is key to efficient inversion in PDE-constrained optimization. Using {\textquoteleft}simultaneous shots{\textquoteright}, or random superposition of source terms, works very well in simple acquisition geometries where all sources see all receivers, but this rarely occurs in practice. We develop an approach that interpolates data to an ideal acquisition geometry while solving the inverse problem using simultaneous shots. The approach is formulated as a joint inverse problem, combining ideas from low-rank interpolation with full-waveform inversion. Results using synthetic experiments illustrate the flexibility and efficiency of the approach.},
	keywords = {Full-waveform inversion, low-rank interpolation, Optimization},
	doi = {10.1088/1361-6420/aaf317},
	url = {https://slim.gatech.edu/Publications/Public/Journals/InverseProblems/2018/liu2018ssi/liu2018ssi.pdf},
	author = {Michelle Liu and Rajiv Kumar and Eldad Haber and Aleksandr Y. Aravkin}
}
@article {haber10TRemp,
	title = {An effective method for parameter estimation with PDE constraints with multiple right hand sides},
	journal = {SIAM Journal on Optimization},
	volume = {22},
	number = {3},
	year = {2012},
	month = {07},
	abstract = {Often, parameter estimation problems of parameter-dependent PDEs involve multiple right-hand sides. The computational cost and memory requirements of such problems increase linearly with the number of right-hand sides. For many applications this is the main bottleneck of the computation. In this paper we show that problems with multiple right-hand sides can be reformulated as stochastic programming problems by combining the right-hand sides into a few {\quotedblbase}simultaneous{\textquotedblright} sources. This effectively reduces the cost of the forward problem and results in problems that are much cheaper to solve. We discuss two solution methodologies: namely sample average approximation and stochastic approximation. To illustrate the effectiveness of our approach we present two model problems, direct current resistivity and seismic tomography.},
	keywords = {FWI, Optimization, SLIM},
	url = {http://dx.doi.org/10.1137/11081126X},
	author = {Eldad Haber and Matthias Chung and Felix J. Herrmann}
}
