@article {kukreja2019PASCccd,
	title = {Combining checkpointing and data compression to accelerate adjoint-based optimization problems},
	journal = {Euro-Par 2019: Parallel Processing},
	year = {2019},
	note = {(Euro-Par 2019: Parallel Processing)},
	pages = {87-100},
	publisher = {Springer International Publishing},
	abstract = {Seismic inversion and imaging are adjoint-based optimization problems that processes up to terabytes of data, regularly exceeding the memory capacity of available computers. Data compression is an effective strategy to reduce this memory requirement by a certain factor, particularly if some loss in accuracy is acceptable. A popular alternative is checkpointing, where data is stored at selected points in time, and values at other times are recomputed as needed from the last stored state. This allows arbitrarily large adjoint computations with limited memory, at the cost of additional recomputations. In this paper we combine compression and checkpointing for the first time to compute a realistic seismic inversion. The combination of checkpointing and compression allows larger adjoint computations compared to using only compression, and reduces the recomputation overhead significantly compared to using only checkpointing.},
	keywords = {Adjoint-state, checkpointing, compression, FD, HPC, Inverse problems},
	doi = {10.1007/978-3-030-29400-7_7},
	url = {https://slim.gatech.edu/Publications/Public/Journals/PASC/2019/kukreja2019PASCccd/kukreja2019PASCccd.pdf},
	author = {Navjot Kukreja and Jan H{\"u}ckelheim and Mathias Louboutin and Paul Hovland and Gerard Gorman}
}
@article {witte2018cls,
	title = {Compressive least-squares migration with on-the-fly Fourier transforms},
	journal = {Geophysics},
	volume = {84},
	number = {5},
	year = {2019},
	note = {(Geophysics)},
	month = {08},
	pages = {R655-R672},
	abstract = {Least-squares reverse-time migration is a powerful approach for true amplitude seismic imaging of complex geological structures, but the successful application of this method is currently hindered by its enormous computational cost, as well as high memory requirements for computing the gradient of the objective function. We tackle these problems by introducing an algorithm for low-cost sparsity-promoting least-squares migration using on-the-fly Fourier transforms. We formulate the least-squares migration objective function in the frequency domain and compute gradients for randomized subsets of shot records and frequencies, thus significantly reducing data movement and the number of overall wave equations solves. By using on-the-fly Fourier transforms, we can compute an arbitrary number of monochromatic frequency-domain wavefields with a time-domain modeling code, instead of having to solve individual Helmholtz equations for each frequency, which quickly becomes computationally infeasible when moving to high frequencies. Our numerical examples demonstrate that compressive imaging with on-the-fly Fourier transforms provides a fast and memory-efficient alternative to time-domain imaging with optimal checkpointing, whose memory requirements for a fixed background model and source wavelet is independent of the number of time steps. Instead, memory and additional computational cost grow with the number of frequencies and determine the amount of subsampling artifacts and crosstalk. In contrast to optimal checkpointing, this offers the possibility to trade both memory and computational cost for image quality or a larger number of iterations and is advantageous in new computing environments such as the cloud, where compute is often cheaper than memory and data movement.},
	keywords = {Fourier, least squares migration, sparsity-promotion},
	doi = {10.1190/geo2018-0490.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2019/witte2018cls/witte2018cls.pdf},
	author = {Philipp A. Witte and Mathias Louboutin and Fabio Luporini and Gerard J. Gorman and Felix J. Herrmann}
}
@article {peters2016cvp,
	title = {Constraints versus penalties for edge-preserving full-waveform inversion},
	journal = {The Leading Edge},
	volume = {36},
	number = {1},
	year = {2017},
	note = {(The Leading Edge)},
	month = {01},
	pages = {94-100},
	abstract = {Full-waveform inversion is challenging in complex geologic areas. Even when provided with an accurate starting model, the inversion algorithms often struggle to update the velocity model. Compared with other areas in applied geophysics, including prior information in full-waveform inversion is still in its relative infancy. In part, this is due to the fact that it is difficult to incorporate prior information that relates to geologic settings where strong discontinuities in the velocity model dominate, because these settings call for nonsmooth regularizations. We tackle this problem by including constraints on the spatial variations and value ranges of the inverted velocities, as opposed to adding penalties to the objective, which is more customary in mainstream geophysical inversion. By demonstrating the lack of predictability of edge-preserving inversion when the regularization is in the form of an added penalty term, we advocate the inclusion of constraints instead. Our examples show that the latter leads to more predictable results and to significant improvements in the delineation of salt bodies when these constraints are relaxed gradually in combination with extending the search space to approximately fit the observed data but not the noise.},
	keywords = {algorithm, full waveform inversion, noise, Optimization, penalty methods, salt dome, total variation},
	doi = {10.1190/tle36010094.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2016/peters2016cvp/peters2016cvp.html},
	author = {Bas Peters and Felix J. Herrmann}
}
@article {esser2016TLEcwi,
	title = {Constrained waveform inversion for automatic salt flooding},
	journal = {The Leading Edge},
	volume = {35},
	number = {3},
	year = {2016},
	note = {(The Leading Edge)},
	month = {03},
	pages = {235-239},
	abstract = {Given appropriate data acquisition, processing to remove nonprimary arrivals, and use of an accurate migration algorithm, it is the quality of the subsurface velocity model that typically controls the quality of imaging that can be obtained from salt-affected seismic data. Full-waveform inversion has the potential to improve the accuracy, resolution, repeatability, and speed with which such velocity models can be generated, but, in the absence of an accurate starting model, that potential is difficult to realize in practice. Presented are successful inversion results, obtained from synthetic subsalt models, using a robust full-waveform inversion code that includes constraints upon the set of allowable earth models. These constraints include limitations on the total variation of the velocity of the model and, most significantly, on the asymmetric variation of velocity with depth such that negative velocity excursions are limited. During the iteration, these constraints are relaxed progressively so that the final model is driven principally by the seismic data, but the constraints act to steer the inversion path away from local minima in its early stages. This methodology is applied to portions of the 2004 BP benchmark and Phase I SEAM salt models, recovering an accurate model of the salt body, including its base and flanks, and an accurate model of the subsalt velocity structure, starting from one-dimensional velocity models that are severely cycle skipped. This approach removes entirely the requirement to pick salt boundaries from migrated seismic data, and acts as a form of automatic salt and sediment flooding during full-waveform inversion.},
	keywords = {FWI, high-contrast and high velocity, salt, total-variation minimization, velocity-model building},
	doi = {10.1190/tle35030235.1},
	url = {http://dx.doi.org/10.1190/tle35030235.1},
	author = {Ernie Esser and Llu{\'\i}s Guasch and Felix J. Herrmann and Mike Warner}
}
@article {vanLeeuwen2014GEOPcav,
	title = {Comment on: {\textquotedblleft}Application of the variable projection scheme for frequency-domain full-waveform inversion{\textquotedblright} (M. Li, J. Rickett, and A. Abubakar, Geophysics, 78, no. 6, R249{\textendash}R257)},
	journal = {Geophysics},
	volume = {79},
	number = {3},
	year = {2014},
	note = {(discussion by Tristan van Leeuwen, Aleksandr Y. Aravkin, and Felix J. Herrmann)},
	month = {05},
	pages = {X11-X17},
	keywords = {variable projection, waveform inversion},
	doi = {10.1190/geo2013-0466.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2014/vanLeeuwen2014GEOPcav/vanLeeuwen2014GEOPcav.pdf},
	author = {Tristan van Leeuwen and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@article {herrmann2011RECORDERcsse2,
	title = {Compressive sensing in seismic exploration: an outlook on a new paradigm},
	journal = {CSEG Recorder},
	volume = {36},
	number = {6},
	year = {2011},
	note = {Part 1 was published in April and Part 2 was published in June},
	month = {06},
	pages = {34-39},
	abstract = {Many seismic exploration techniques rely on the collection of massive data volumes that are subsequently mined for information during processing. While this approach has been extremely successful in the past, current efforts toward higher resolution images in increasingly complicated regions of the Earth continue to reveal fundamental shortcomings in our workflows. Chiefly amongst these is the so-called "curse of dimensionality" exemplified by Nyquist{\textquoteright}s sampling criterion, which disproportionately strains current acquisition and processing systems as the size and desired resolution of our survey areas continues to increase. We offer an alternative sampling method leveraging recent insights from compressive sensing towards seismic acquisition and processing for data that, from a traditional point of view, are considered to be undersampled. The main outcome of this approach is a new technology where acquisition and processing related costs are decoupled the stringent Nyquist sampling criterion. At the heart of our approach lies randomized incoherent sampling that breaks subsampling-related interferences by turning them into harmless noise, which we subsequently remove by promoting sparsity in a transform-domain. Acquisition schemes designed to fit into this regime no longer grow significantly in cost with increasing resolution and dimensionality of the survey area, but instead its cost ideally only depends on transform-domain sparsity of the expected data. Our contribution is twofold. First, we demonstrate by means of carefully designed numerical experiments that ideas from compressive sensing can be adapted to seismic acquisition. Second, we leverage the property that seismic data volumes are well approximated by a small percentage of curvelet coefficients. Thus curvelet-domain sparsity allows us to recover conventionally-sampled seismic data volumes from compressively-sampled data volumes whose size exceeds this percentage by only a small factor. Because compressive sensing combines transformation and encoding by a single linear encoding step, this technology is directly applicable to seismic acquisition and therefore constitutes a new paradigm where acquisitions costs scale with transform-domain sparsity instead of the gridsize. We illustrate this principle by showcasing recovery of a real seismic line from simulated compressively sampled acquisitions.},
	url = {http://csegrecorder.com/articles/view/compressive-sensing-in-seismic-exploration-an-outlook-on-a-new-paradigm},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/CSEGRecorder/2011/herrmann2011RECORDERcsse/herrmann2011RECORDERcsse.pdf},
	author = {Felix J. Herrmann and Haneet Wason and Tim T.Y. Lin}
}
@article {herrmann2011RECORDERcsse1,
	title = {Compressive sensing in seismic exploration: an outlook on a new paradigm},
	journal = {CSEG Recorder},
	volume = {36},
	number = {4},
	year = {2011},
	note = {Part 1 was published in April and Part 2 was published in June},
	month = {04},
	pages = {19-33},
	abstract = {Many seismic exploration techniques rely on the collection of massive data volumes that are subsequently mined for information during processing. While this approach has been extremely successful in the past, current efforts toward higher resolution images in increasingly complicated regions of the Earth continue to reveal fundamental shortcomings in our workflows. Chiefly amongst these is the so-called "curse of dimensionality" exemplified by Nyquist{\textquoteright}s sampling criterion, which disproportionately strains current acquisition and processing systems as the size and desired resolution of our survey areas continues to increase. We offer an alternative sampling method leveraging recent insights from compressive sensing towards seismic acquisition and processing for data that, from a traditional point of view, are considered to be undersampled. The main outcome of this approach is a new technology where acquisition and processing related costs are decoupled the stringent Nyquist sampling criterion. At the heart of our approach lies randomized incoherent sampling that breaks subsampling-related interferences by turning them into harmless noise, which we subsequently remove by promoting sparsity in a transform-domain. Acquisition schemes designed to fit into this regime no longer grow significantly in cost with increasing resolution and dimensionality of the survey area, but instead its cost ideally only depends on transform-domain sparsity of the expected data. Our contribution is split into two part.},
	url = {http://csegrecorder.com/articles/view/compressive-sensing-in-seismic-exploration-outlook-on-a-new-paradigm},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/CSEGRecorder/2011/herrmann2011RECORDERcsse/herrmann2011RECORDERcsse.pdf},
	author = {Felix J. Herrmann and Haneet Wason and Tim T.Y. Lin}
}
@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 {herrmann2009GEOPcbm,
	title = {Curvelet-based migration preconditioning and scaling},
	journal = {Geophysics},
	volume = {74},
	year = {2009},
	month = {07-08},
	pages = {A41-A46},
	abstract = {The extremely large size of typical seismic imaging problems has been one of the major stumbling blocks for iterative techniques to attain accurate migration amplitudes. These iterative methods are important because they complement theoretical approaches that are hampered by difficulties to control problems such as finite-acquisition aperture, source-receiver frequency response, and directivity. To solve these problems, we apply preconditioning, which significantly improves convergence of least-squares migration. We discuss different levels of preconditioning that range from corrections for the order of the migration operator to corrections for spherical spreading, and position and reflector-dip dependent amplitude errors. While the first two corrections correspond to simple scalings in the Fourier and physical domain, the third correction requires phase-space (space spanned by location and dip) scaling, which we carry out with curvelets. We show that our combined preconditioner leads to a significant improvement of the convergence of least-squares {\textquoteleft}wave-equation{\textquoteright} migration on a line from the SEG AA{\textquoteright} salt model.},
	keywords = {Imaging, migration, SLIM},
	doi = {10.1190/1.3124753},
	url = {http://geophysics.geoscienceworld.org/content/74/4/A41.abstract},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2009/herrmann2009GEOPcbm/herrmann2009GEOPcbm.pdf},
	author = {Felix J. Herrmann and Cody R. Brown and Yogi A. Erlangga and Peyman P. Moghaddam}
}
@article {herrmann2008GEOPcbs,
	title = {Curvelet-based seismic data processing: a multiscale and nonlinear approach},
	journal = {Geophysics},
	volume = {73},
	number = {1},
	year = {2008},
	month = {03},
	pages = {A1-A5},
	publisher = {SEG},
	abstract = {Mitigating missing data, multiples, and erroneous migration amplitudes are key factors that determine image quality. Curvelets, little {\textquoteleft}{\textquoteleft}plane waves,{\textquoteright}{\textquoteright} complete with oscillations in one direction and smoothness in the other directions, sparsify a property we leverage explicitly with sparsity promotion. With this principle, we recover seismic data with high fidelity from a small subset (20\%) of randomly selected traces. Similarly, sparsity leads to a natural decorrelation and hence to a robust curvelet-domain primary-multiple separation for North Sea data. Finally, sparsity helps to recover migration amplitudes from noisy data. With these examples, we show that exploiting the curvelet{\textquoteright}s ability to sparsify wavefrontlike features is powerful, and our results are a clear indication of the broad applicability of this transform to exploration seismology. \copyright2008 Society of Exploration Geophysicists},
	keywords = {Acquisition, curvelet transform, Processing, SLIM},
	doi = {10.1190/1.2799517},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/herrmann08GEOcbs/herrmann08GEOcbs.pdf},
	author = {Felix J. Herrmann and Deli Wang and Gilles Hennenfent and Peyman P. Moghaddam}
}
@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}
}
