@article {herrmann2009GEOPcsf,
	title = {Compressive simultaneous full-waveform simulation},
	journal = {Geophysics},
	volume = {74},
	number = {4},
	year = {2009},
	month = {07-08},
	pages = {A35-A40},
	abstract = {The fact that computational complexity of wavefield simulation is proportional to the size of the discretized model and acquisition geometry, and not to the complexity of the simulated wavefield, is a major impediment within seismic imaging. By turning simulation into a compressive sensing problem{\textendash}-where simulated data is recovered from a relatively small number of independent simultaneous sources{\textendash}-we remove this impediment by showing that compressively sampling a simulation is equivalent to compressively sampling the sources, followed by solving a reduced system. As in compressive sensing, this allows for a reduction in sampling rate and hence in simulation costs. We demonstrate this principle for the time-harmonic Helmholtz solver. The solution is computed by inverting the reduced system, followed by a recovery of the full wavefield with a sparsity promoting program. Depending on the wavefield{\textquoteright}s sparsity, this approach can lead to significant cost reductions, in particular when combined with the implicit preconditioned Helmholtz solver, which is known to converge even for decreasing mesh sizes and increasing angular frequencies. These properties make our scheme a viable alternative to explicit time-domain finite-differences.},
	keywords = {Compressive Sensing, full-waveform, Modelling, SLIM},
	doi = {10.1190/1.3115122},
	url = {http://library.seg.org/doi/abs/10.1190/1.3115122},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2009/herrmann2009GEOPcsf/herrmann2009GEOPcsf.pdf},
	author = {Felix J. Herrmann and Yogi A. Erlangga and Tim T.Y. Lin}
}
@article {lin2007GEOPcwe,
	title = {Compressed wavefield extrapolation},
	journal = {Geophysics},
	volume = {72},
	number = {5},
	year = {2007},
	month = {08},
	pages = {SM77-SM93},
	publisher = {SEG},
	abstract = {An explicit algorithm for the extrapolation of one-way wavefields is proposed that combines recent developments in information theory and theoretical signal processing with the physics of wave propagation. Because of excessive memory requirements, explicit formulations for wave propagation have proven to be a challenge in 3D. By using ideas from compressed sensing, we are able to formulate the (inverse) wavefield extrapolation problem on small subsets of the data volume, thereby reducing the size of the operators. Compressed sensing entails a new paradigm for signal recovery that provides conditions under which signals can be recovered from incomplete samplings by nonlinear recovery methods that promote sparsity of the to-be-recovered signal. According to this theory, signals can be successfully recovered when the measurement basis is incoherent with the representa-tion in which the wavefield is sparse. In this new approach, the eigenfunctions of the Helmholtz operator are recognized as a basis that is incoherent with curvelets that are known to compress seismic wavefields. By casting the wavefield extrapolation problem in this framework, wavefields can be successfully extrapolated in the modal domain, despite evanescent wave modes. The degree to which the wavefield can be recovered depends on the number of missing (evanescent) wavemodes and on the complexity of the wavefield. A proof of principle for the compressed sensing method is given for inverse wavefield extrapolation in 2D, together with a pathway to 3D during which the multiscale and multiangular properties of curvelets, in relation to the Helmholz operator, are exploited. The results show that our method is stable, has reduced dip limitations, and handles evanescent waves in inverse extrapolation. \copyright2007 Society of Exploration Geophysicists},
	keywords = {Modelling, SLIM, wave propagation},
	doi = {10.1190/1.2750716},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2007/lin07cwe/lin07cwe.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
