@conference {siahkoohi2022EAGEweb,
	title = {Wave-equation based inversion with amortized variational Bayesian inference},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2022},
	note = {(EAGE, Madrid)},
	month = {06},
	pages = {Session 2: Velocity model building and imaging (different domains)},
	abstract = {Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth{\textquoteright}s highly heterogeneous structure is unknown, present a challenge in encoding prior knowledge through analytical expressions. Our main contribution is a generative-model-based regularization approach, robust to out-of-distribution data, which exploits the prior knowledge embedded in existing data and model pairs. Utilizing an amortized variational inference objective, a conditional normalizing flow (NF) is pretrained on pairs of low- and high-fidelity migrated images in order to achieve a low-fidelity approximation to the seismic imaging posterior distribution for previously unseen data. The NF is used after pretraining to reparameterize the unknown seismic image in an inversion scheme involving physics-guided data misfit and a Gaussian prior on the NF latent variable. Solving this optimization problem with respect to the latent variable enables us to leverage the benefits of data-driven conditional priors whilst being informed by physics and data. The numerical experiments demonstrate that the proposed inversion scheme produces seismic images with limited artifacts when dealing with noisy and out-of-distribution data.},
	keywords = {conditional priors, EAGE, Normalizing flows, seismic imaging},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2022/siahkoohi2022EAGEweb/abstract.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2022/siahkoohi2022EAGEweb/Mon-Herrmann.pdf},
	software = {https://github.com/slimgroup/ConditionalNFs4Imaging.jl},
	author = {Ali Siahkoohi and Rafael Orozco and Gabrio Rizzuti and Felix J. Herrmann}
}
@conference {zhang2020SEGwrw,
	title = {Wavefield recovery with limited-subspace weighted matrix factorizations},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2020},
	note = {(SEG, virtual)},
	month = {09},
	pages = {2858-2862},
	abstract = {Modern-day seismic imaging and monitoring technology increasingly rely on dense full-azimuth sampling. Unfortunately, the costs of acquiring densely sampled data rapidly become prohibitive and we need to look for ways to sparsely collect data, e.g. from sparsely distributed ocean bottom nodes, from which we then derive densely sampled surveys through the method of wavefield reconstruction. Because of their relatively cheap and simple calculations, wavefield reconstruction via matrix factorizations has proven to be a viable and scalable alternative to the more generally used transform-based methods. While this method is capable of processing all full azimuth data frequency by frequency slice, its performance degrades at higher frequencies because monochromatic data at these frequencies is not as well approximated by low-rank factorizations. We address this problem by proposing a recursive recovery technique, which involves weighted matrix factorizations where recovered wavefields at the lower frequencies serve as prior information for the recovery of the higher frequencies. To limit the adverse effects of potential overfitting, we propose a limited-subspace recursively weighted matrix factorization approach where the size of the row and column subspaces to construct the weight matrices is constrained. We apply our method to data collected from the Gulf of Suez, and our results show that our limited-subspace weighted recovery method significantly improves the recovery quality.},
	keywords = {algorithm, data reconstruction, frequency-domain, interpolation, Processing, SEG},
	doi = {10.1190/segam2020-3428365.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/zhang2020SEGwrw/zhang2020SEGwrw.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/zhang2020SEGwrw/zhang2020SEGwrw_pres.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/zhang2020SEGwrw/zhang2020SEGwrw_pres.mp4},
	software = {https://github.com/slimgroup/Software.SEG2020},
	author = {Yijun Zhang and Shashin Sharan and Oscar Lopez and Felix J. Herrmann}
}
@conference {siahkoohi2020SEGwdp,
	title = {Weak deep priors for seismic imaging},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2020},
	note = {(SEG, virtual)},
	month = {09},
	pages = {2998-3002},
	abstract = {Incorporating prior knowledge on model unknowns of interest is essential when dealing with ill-posed inverse problems due to the nonuniqueness of the solution and data noise. Unfortunately, it is not trivial to fully describe our priors in a convenient and analytical way. Parameterizing the unknowns with a convolutional neural network (CNN), and assuming an uninformative Gaussian prior on its weights, leads to a variational prior on the output space that favors "natural" images and excludes noisy artifacts, as long as overfitting is prevented. This is the so-called deep-prior approach. In seismic imaging, however, evaluating the forward operator is computationally expensive, and training a randomly initialized CNN becomes infeasible. We propose, instead, a weak version of deep priors, which consists of relaxing the requirement that reflectivity models must lie in the network range, and letting the unknowns deviate from the network output according to a Gaussian distribution. Finally, we jointly solve for the reflectivity model and CNN weights. The chief advantage of this approach is that the updates for the CNN weights do not involve the modeling operator, and become relatively cheap. Our synthetic numerical experiments demonstrate that the weak deep prior is more robust with respect to noise than conventional least-squares imaging approaches, with roughly twice the computational cost of reverse-time migration, which is the affordable computational budget in large-scale imaging problems.},
	keywords = {deep prior, machine learning, SEG, seismic imaging},
	doi = {10.1190/segam2020-3417568.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/siahkoohi2020SEGwdp/siahkoohi2020SEGwdp.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/siahkoohi2020SEGwdp/siahkoohi2020SEGwdp_pres.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/siahkoohi2020SEGwdp/siahkoohi2020SEGwdp_pres.mp4},
	software = {https://github.com/slimgroup/Software.SEG2020},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Felix J. Herrmann}
}
@conference {herrmann2015SIAMwri,
	title = {Wavefield Reconstruction Inversion {\textendash} reaping the benefits from extending the search space},
	booktitle = {SIAM Conference on Mathematical and Computational Issues in the Geosciences},
	year = {2015},
	note = {(SIAM Conference on Mathematical and Computational Issues in the Geosciences, Stanford University, California)},
	month = {06-07},
	keywords = {SIAM, WRI},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2015/herrmann2015SIAMwri/herrmann2015SIAMwri_pres.pdf},
	author = {Felix J. Herrmann}
}
@conference {herrmann2015IIPFWIwcc,
	title = {Wavefield Reconstruction Inversion with convex constraints},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {During this talk, we discuss how to exploit the special structure of Wavefield Reconstruction Inversion (WRI) to include convex bound and total-variation constraints in a computationally feasible manner. The resulting method shows promising results on challenging models that include high-velocity high-contrast inclusions such as salt or basalt. This is joint work with Ernie Esser who passed away and who is dearly missed.},
	keywords = {convex, FWI, regularization},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/herrmann2015IIPFWIwcc/herrmann2015IIPFWIwcc_pres.pdf},
	author = {Felix J. Herrmann and Ernie Esser and Llu{\'\i}s Guasch}
}
@conference {fang2015IIPFWIwri,
	title = {Wavefield Reconstruction Inversion with source estimation and its application to 2014 Chevron synthetic blind test dataset},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {We present a robust wavefield reconstruction inversion with source estimation. The source wavelet is estimated with the reconstruction of wavefield simultaneously by solving an extended data augmentation problem. We apply this method to the 2014 Chevron synthetic blind test dataset and show the robustness of our method.},
	keywords = {FWI, source estimation, WRI},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/fang2015IIPFWIwri/fang2015IIPFWIwri_pres.pdf},
	author = {Zhilong Fang and Felix J. Herrmann}
}
@conference {wang2015SIAMwds,
	title = {Wavefield-denoising and source encoding},
	booktitle = {SIAM Conference on Mathematical and Computational Issues in the Geosciences},
	year = {2015},
	note = {(SIAM Conference on Mathematical and Computational Issues in the Geosciences, Stanford University, California)},
	month = {06-07},
	keywords = {SIAM, source encoding, WRI},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2015/wang2015SIAMwds/wang2015SIAMwds_pres.pdf},
	author = {Rongrong Wang and Ozgur Yilmaz and Felix J. Herrmann}
}
@conference {peters2015AIPwri,
	title = {Wavefield-reconstruction inversion},
	booktitle = {Conference on Applied Inverse Problems},
	year = {2015},
	note = {(AIP, Helsinki)},
	month = {05},
	abstract = {Wavefield Reconstruction Inversion is a method for PDE-constrained optimization, which revolves around the estimation of fields using the PDE as well as the observed data in a least-squares sense. The method is quadratic penalty based, which offers some interesting possibilities for the construction of algorithms, compared to the Lagrangian form. One of the main benefits of the method is when the initial guess is far from the global minimizer. Reduced-space and full-space algorithms are discussed, including illustrative examples. The method was developed with seismic applications in mind, but applies to other PDE-constrained optimization problems as well.},
	keywords = {AIP, Full-waveform inversion, Optimization, penalty method, Waveform reconstruction inversion},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/AIP/2015/peters2015AIPwri/peters2015AIPwri.pdf},
	author = {Bas Peters and Felix J. Herrmann}
}
@conference {herrmann2015IIPFWIwri,
	title = {Wavefield-Reconstruction Inversion {\textemdash} WRI},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {We discuss a recently proposed novel method for waveform inversion: Wavefield Reconstruction Inversion (WRI). As opposed to conventional FWI {\textemdash} which attempts to minimize the error between observed and predicted data obtained by solving a wave equation {\textendash} WRI reconstructs a wave-field from the data and extracts a model-update from this wavefield by minimizing the wave-equation residual. The method does not require explicit computation of an adjoint wavefield as all the necessary information is contained in the reconstructed wavefield. We show how the corresponding model updates can be interpreted physically analogously to the conventional imaging-condition-based approach.},
	keywords = {FWI, inversion, WRI},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/herrmann2015IIPFWIwri/herrmann2015IIPFWIwri_pres.pdf},
	author = {Felix J. Herrmann}
}
@conference {peters2014EAGEweb,
	title = {Wave-equation based inversion with the penalty method: adjoint-state versus wavefield-reconstruction inversion},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2014},
	month = {06},
	abstract = {In this paper we make a comparison between wave-equation based inversions based on the adjoint-state and penalty methods. While the adjoint-state method involves the minimization of a data-misfit and exact solutions of the wave-equation for the current velocity model, the penalty-method aims to first find a wavefield that jointly fits the data and honours the physics, in a least-squares sense. Given this reconstructed wavefield, which is a proxy for the true wavefield in the true model, we calculate updates for the velocity model. Aside from being less nonlinear{\textendash}the acoustic wave equation is linear in the wavefield and model parameters but not in both{\textendash}the inversion is carried out over a solution space that includes both the model and the wavefield. This larger search space allows the algortihm to circumnavigate local minima, very much in the same way as recently proposed model extentions try to acomplish. We include examples for low frequencies, where we compare full-waveform inversion results for both methods, for good and bad starting models, and for high frequencies where we compare reverse-time migration with linearized imaging based on wavefield-reconstruction inversion. The examples confirm the expected benefits of the proposed method.},
	keywords = {EAGE, Full-waveform inversion, Imaging, Optimization, penalty method},
	doi = {10.3997/2214-4609.20140704},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/peters2014EAGEweb/peters2014EAGEweb.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/peters2014EAGEweb/peters2014EAGEweb_pres.pdf},
	author = {Bas Peters and Felix J. Herrmann and Tristan van Leeuwen}
}
@conference {herrmann2014SEGWS,
	title = {Wavefield Reconstruction Inversion (WRI) {\textendash} a new take on wave-equation based inversion},
	booktitle = {SEG Workshop on Full Waveform Inversion - Elastic Approaches and Issues with Anisotropy, Nonshallow Inversion, Poor Starting Model; Denver},
	year = {2014},
	note = {(SEG Workshop, Denver)},
	month = {10},
	keywords = {FWI, SEG, workshop, WRI},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/herrmann2014SEGWSwri/herrmann2014SEGWSwri_pres.pdf},
	author = {Felix J. Herrmann and Ernie Esser and Tristan van Leeuwen and Bas Peters}
}
@conference {vanleeuwen2012EAGEext,
	title = {Wave-equation extended images: computation and velocity continuation},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2012},
	month = {06},
	abstract = {An extended image is a multi-dimensional correlation of source and receiver wavefields. For a kinematically correct velocity, most of the energy will be concentrated at zero offset. Because of the computational cost involved in correlating the wavefields for all offsets, such exteded images are computed for a subsurface offset that is aligned with the local dip. In this paper, we present an efficient way to compute extended images for all subsurface offsets without explicitly calculating the receiver wavefields, thus making it computationally feasible to compute such extended images. We show how more conventional image gathers, where the offset is aligned with the dip, can be extracted from this extended image. We also present a velocity continuation procedure that allows us to compute the extended image for a given velocity without recomputing all the source wavefields.},
	keywords = {EAGE, extended image, velocity continuation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2012/vanleeuwen2012EAGEext/vanleeuwen2012EAGEext.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2012/vanleeuwen2012EAGEext/vanleeuwen2012EAGEext_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=59616},
	author = {Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {Mansour11TRwmmw,
	title = {Weighted -$\ell_1$ minimization with multiple weighting sets},
	booktitle = {Proc. SPIE},
	volume = {8138},
	year = {2011},
	month = {09},
	pages = {813809-813809-13},
	abstract = {In this paper, we study the support recovery conditions of weighted -$\ell_1$ minimization for signal reconstruction from compressed sensing measurements when multiple support estimate sets with different accuracy are available. We identify a class of signals for which the recovered vector from -$\ell_1$ minimization provides an accurate support estimate. We then derive stability and robustness guarantees for the weighted -$\ell_1$ minimization problem with more than one support estimate. We show that applying a smaller weight to support estimate that enjoy higher accuracy improves the recovery conditions compared with the case of a single support estimate and the case with standard, i.e., non-weighted,-$\ell_1$ minimization. Our theoretical results are supported by numerical simulations on synthetic signals and real audio signals.},
	keywords = {Compressive Sensing, Optimization},
	doi = {10.1117/12.894165},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SPIE/2011/Mansour11TRwmmw/Mansour11TRwmmw.pdf},
	author = {Hassan Mansour and Ozgur Yilmaz}
}
@conference {yan2008SINBADwru,
	title = {Wavefield reconstruction using simultaneous denoising interpolation vs. denoising after interpolation},
	booktitle = {SINBAD 2008},
	year = {2008},
	abstract = {This report represents and compares two methods of wavefield reconstruction from noisy seismic data with missing traces. The two methods are (i) First interpolate incomplete noisy data to get complete noisy data and then denoise, and (ii) Interpolate and denoise the incomplete noisy data simultaneously. A sample test of synthetic data will be presented. The results of tests show that denoising after interpolation is better than simultaneous denoising and interpolation if the parameter of the denoising problem is chosen appropriately.},
	keywords = {Presentation, SINBAD, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2008/yan2008SINBADwru/yan2008SINBADwru.pdf},
	author = {Jiupeng Yan}
}
