@conference {orozco2023AABIiter,
	title = {Refining Amortized Posterior Approximations using Gradient-Based Summary Statistics},
	booktitle = {5th Symposium on Advances in Approximate Bayesian Inference},
	year = {2023},
	note = {(AABI, Honolulu)},
	month = {06},
	abstract = {We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in maximally informative summary statistics. Amortized variational inference is restricted by the expressive power of the chosen variational distribution and the availability of training data in the form of joint data and parameter samples, which often lead to approximation errors such as the amortization gap. To address this issue, we propose an iterative framework that refines the current amortized posterior approximation at each step. Our approach involves alternating between two steps: (1) constructing a training dataset consisting of pairs of summarized data residuals and parameters, where the summarized data residual is generated using a gradient-based summary statistic, and (2) training a conditional generative model {\textendash} a normalizing flow in our examples {\textendash} on this dataset to obtain a probabilistic update of the unknown parameter. This procedure leads to iterative refinement of the amortized posterior approximations without the need for extra training data. We validate our method in a controlled setting by applying it to a stylized problem, and observe improved posterior approximations with each iteration. Additionally, we showcase the capability of our method in tackling realistically sized problems by applying it to transcranial ultrasound, a high-dimensional, nonlinear inverse problem governed by wave physics, and observe enhanced posterior quality through better image reconstruction with the posterior mean.},
	keywords = {AABI, Amortization Gap, Amortized Variational Inference, Bayesian inference, conditional normalizing flows, Summary Statistics},
	url = {https://arxiv.org/abs/2305.08733},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/AABI/2023/orozco2023AABIiter/aabi_poster.pdf},
	author = {Rafael Orozco and Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@conference {siahkoohi2022SEGWSrav,
	title = {Reliable amortized variational inference with conditional normalizing flows via physics-based latent distribution correction},
	booktitle = {IMAGE Workshop on Subsurface Uncertainty Description and Estimation - Moving Away from Single Prediction with Distribution Learning},
	year = {2022},
	note = {(IMAGE Workshop, Houston)},
	month = {09},
	abstract = {Bayesian inference for high-dimensional inverse problems is challenged by the computational costs associated with the forward operator during posterior sampling, as well as the selection of an appropriate prior distribution that encodes our prior knowledge about the unknown. Amortized variational inference addresses these challenges by pretraining a conditional normalizing flow (cNF) that approximates the posterior distribution over the existing model and data joint samples where the prior is implicitly learned from the data. When fed data and normally distributed latent samples as input, the pretrained cNF provides posterior samples for previously unseen data virtually for free. The accuracy of this purely data-driven approach, however, is dependent on the availability of high-fidelity training data, which is rarely the case with geophysical inverse problems, due to the highly heterogeneous structure of the Earth. To overcome this challenge and to minimize the negative bias of data distribution shifts during inference, we propose learning a physics-based correction to the cNF latent distribution to provide a more accurate approximation to the posterior distribution. We accomplish this by parameterizing the cNF latent distribution by a Gaussian distribution with an unknown mean and diagonal covariance, which are estimated by minimizing the Kullback-Leibler divergence between the corrected posterior distribution estimate and the true posterior distribution. For a relatively well-trained cNF, this approach provides reliable posterior samples with a limited computational cost while remaining bound to data and physics. We showcase the computational gains of this approach on a "quasi" real seismic imaging example.},
	keywords = {Bayesian inference, deep learning, Generative models, Imaging, Inverse problems, SEG, Uncertainty quantification, workshop},
	url = {https://www.imageevent.org/Workshop/subsurface-uncertainty-description-estimation-moving-away-single-prediction-distribution-learning},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/siahkoohi2022SEGWSrav/Thur-15-55-Siahkoohi.pdf},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Rafael Orozco and Felix J. Herrmann}
}
@conference {yang2018SEGrde,
	title = {Removing density effects in LS-RTM with a low-rank matched filter},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2018},
	note = {(SEG, Anaheim)},
	month = {10},
	pages = {4251-4255},
	abstract = {Least-squares reverse-time migration faces difficulties when it inverts the data containing strong components related to density variation with velocity-only Born modeling operator. The strong density perturbation will be inverted as strong dummy velocity perturbations, which influence the amplitudes and phase of the velocity perturbations in the inverted model. The traditional method is to invert the additional density variations by developing Born operator with respect to both density and velocity or modify the image condition. In this work, we develop a matched-filter based LS-RTM for velocity-only Born modeling operator, which removes the artifacts in the imaging created by the strong density variation. This method doesn{\textquoteright}t call for extra work of finite difference stencil and is more general. In the experiment part, we use a complex discontinuous layered medium with strong density variations at the ocean bottom, and show the efficacy of the propose formulation.},
	keywords = {density effect, Least square, low rank, SEG},
	doi = {10.1190/segam2018-2997814.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2018/yang2018SEGrde/yang2018SEGrde.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2018/yang2018SEGrde/yang2018SEGrde_pres.pdf},
	author = {Mengmeng Yang and Rajiv Kumar and Rongrong Wang and Felix J. Herrmann}
}
@conference {louboutin2017SIAMras,
	title = {Raising the abstraction to separate concerns: enabling different physics for geophysical exploration},
	booktitle = {SIAM Conference on Computational Science and Engineering},
	year = {2017},
	note = {(SIAM Conference on Computational Science and Engineering, Atlanta)},
	month = {02-03},
	abstract = {Full-waveform inversion is a PDE-constrained optimisation problem involving massive amounts of data (petabytes) and large numbers of unknowns (O(10^9)). This well known compute-intensive and data-intensive is extremely challenging for several reasons. First, there is the complexity of having to handle extremely large data volumes with metadata related to experimental details in the field, and the discretization of the unknown earth parameters and approximate physics. Second, reduced or adjoint-state methods call for computationally intensive PDE solves for each source experiment (of which there are thousands) for each iteration of a gradient-based optimization scheme. The talks will give an overview how carefully chosen layers of abstraction can help manage both the complexity and scale of inversion while still achieving the high degree of computational performance required to make full-waveform a practical tool. Specifically, the presentations will focus on domain specific stencil language for time-stepping methods to solve various types of wave equations and on abstracts for large-scale parallel optimization frameworks.},
	keywords = {finite differences, HPC, Modelling, SIAM, time domain},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2017/louboutin2017SIAMras/louboutin2017SIAMras_pres.mov},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2017/louboutin2017SIAMras/louboutin2017SIAMras_pres.pdf},
	author = {Mathias Louboutin and Michael Lange and Navjot Kukreja and Fabio Luporini and Felix J. Herrmann and Gerard Gorman}
}
@conference {alfaraj2017SEGrsw,
	title = {Reconstruction of S-waves from low-cost randomized and simultaneous acquisition by joint sparse inversion},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2017},
	note = {(SEG, Houston)},
	month = {09},
	pages = {2533-2538},
	abstract = {Spatial Nyquist sampling rate, which is proportional to the apparent subsurface velocity, is the key deciding cost factor for conventional seismic acquisition. Due to the lower shear wave velocity compared with compressional waves, finer spatial sampling is required to properly record the earlier, which increases the acquisition costs. This is one of the reasons why shear waves are usually not considered in practice. To avoid having the Nyquist criterion as the deciding cost factor and to utilize multicomponent data to its available full extent, we propose acquiring randomly undersampled ocean bottom seismic data. Each component can then be interpolated separately, followed by elastic decomposition to recover up- and down-going S-waves. Instead, we jointly interpolate and decompose the recorded multicomponent data by solving one sparsity promoting optimization problem. This way we ensure that the relative amplitudes of the multicomponent data is preserved. We compare two sparsifying transforms: the curvelet transform and the frequency-wavenumber transform. Another key cost deciding factor for seismic acquisition is the efficiency of acquiring data. This calls for simultaneous acquisition, which requires a source separation step. Similarly, instead of taking a two-step approach, we perform a sparsity-promoting joint source separation decomposition. Results on economically and efficiently acquired synthetic data of both joint methods show their ability of reconstructing accurate up- and down-going S-waves.},
	keywords = {decomposition, elastic, interpolation, randomized acquisition, SEG, shear wave, source separation, sparse},
	doi = {10.1190/segam2017-17681376.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/alfaraj2017SEGrsw/alfaraj2017SEGrsw.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/alfaraj2017SEGrsw/alfaraj2017SEGrsw_pres.pdf},
	author = {Ali M. Alfaraj and Rajiv Kumar and Felix J. Herrmann}
}
@conference {herrmann2015ASEGrae,
	title = {Randomized algorithms in exploration seismology},
	booktitle = {ASEG Annual Conference Proceedings},
	year = {2015},
	note = {(ASEG, Perth)},
	month = {02},
	abstract = {As in several other industries, progress in exploration seismology relies on the collection and processing of massive data volumes that grow exponentially in size as the survey area and desired resolution increase. This exponential growth {\textendash}- in combination with the increased complexity of the next-generation of iterative wave-equation based inversion algorithms {\textendash}- puts strains on our acquisition systems and computational back ends impeding progress in our field. During this talk, I will review how recent randomized algorithms from Compressive Sensing and Machine learning can be used to overcome some of these challenges by fundamentally rethinking how we sample and process seismic data. The key idea here is to reduce acquisition and computational costs by deliberately working on small randomized subsets of the data at a desired accuracy. I will illustrate these concepts using a variety of compelling examples on realistic synthetics and field data.},
	keywords = {Acquisition, ASEG, compressed sensing, FWI, Imaging, seismology},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ASEG/2015/herrmann2015ASEGrae/herrmann2015ASEGrae.pdf},
	author = {Felix J. Herrmann}
}
@conference {herrmann2015IIPFWIras,
	title = {Randomized algorithms in seismic imaging},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {As in several other industries, progress in exploration seismology relies on the collection and processing of massive data volumes that grow exponentially in size as the survey area and desired resolution increase. This exponential growth {\textendash} in combination with the increased complexity of the next-generation of iterative wave-equation based inversion algorithms {\textendash} puts strains on our acquisition systems and computational back ends impeding progress in our field. During this talk, I will review how recent randomized algorithms from Compressive Sensing and Machine learning can be used to overcome some of these challenges by fundamentally rethinking how we sample and process seismic data. The key idea here is to reduce acquisition and computational costs by deliberately working on small randomized subsets of the data at a desired accuracy. I will illustrate these concepts using a variety of compelling examples on realistic synthetics and field data.},
	keywords = {FWI, Imaging, randomization, seismic},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/herrmann2015IIPFWIras/herrmann2015IIPFWIras_pres.pdf},
	author = {Felix J. Herrmann}
}
@conference {kumar2015IIPFWIrmb,
	title = {Rank minimization based seismic data processing and inversion},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {We present the low-rank extensions of full-waveform inversion to mitigate the local-minima issues. The purpose formulation is computationally tractable and does not involve any extra computational cost compared to the adjoint-state method.},
	keywords = {FWI, inversion, Processing, rank minimization},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/kumar2015IIPFWIrmb/kumar2015IIPFWIrmb_pres.pdf},
	author = {Rajiv Kumar and Curt Da Silva and Oscar Lopez and Aleksandr Y. Aravkin and Hassan Mansour and Haneet Wason and Ernie Esser and Felix J. Herrmann}
}
@conference {lopez2015EAGErma,
	title = {Rank minimization via alternating optimization: seismic data interpolation},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2015},
	note = {(EAGE, Madrid)},
	month = {06},
	abstract = {Low-rank matrix completion techniques have recently become an effective tool for seismic trace interpolation problems. In this talk, we consider an alternating optimization scheme for nuclear norm minimization and discuss the applications to large scale wave field reconstruction. By adopting a factorization approach to the rank minimization problem we write our low-rank matrix in bi-linear form, and modify this workflow by alternating our optimization to handle a single matrix factor at a time. This allows for a more tractable procedure that can robustly handle large scale, highly oscillatory and critically subsampled seismic data sets. We demonstrate the potential of this approach with several numerical experiments on a seismic line from the Nelson 2D data set and a frequency slice from the Gulf of Mexico data set.},
	keywords = {EAGE, interpolation, low-rank, matrix completion},
	doi = {10.3997/2214-4609.201413453},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/lopez2015EAGErma/lopez2015EAGErma.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/lopez2015EAGErma/lopez2015EAGErma_poster.pdf},
	author = {Oscar Lopez and Rajiv Kumar and Felix J. Herrmann}
}
@conference {louboutin2015IIPFWIrwi,
	title = {Regularizing waveform inversion by projections onto convex sets},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {A framework is proposed for regularizing the waveform inversion problem by projections onto intersections of convex sets. Multiple pieces of prior information about the geology are represented by multiple convex sets, for example limits on the velocity or minimum smoothness conditions on the model. The data-misfit is then minimized, such that the estimated model is always in the intersection of the convex sets. Therefore, it is clear what properties the estimated model will have at each iteration. This approach does not require any quadratic penalties to be used and thus avoids the known problems and limitations of those types of penalties. It is shown that by formulating waveform inversion as a constrained problem, regularization ideas such as Tikhonov regularization and gradient filtering can be incorporated into one framework. The algorithm is generally applicable, in the sense that it works with any (differentiable) objective function and does not require significant additional computation. The method is demonstrated on the inversion of the 2D marine isotropic elastic synthetic seismic benchmark by Chevron using an acoustic modeling code. To highlight the effect of the projections, we apply no data pre-processing. This is joint work with Bas Peters.},
	keywords = {convex, FWI, regularization},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/louboutin2015IIPFWIrwi/louboutin2015IIPFWIrwi_pres.pdf},
	author = {Mathias Louboutin and Bas Peters and Brendan R. Smithyman and Felix J. Herrmann}
}
@conference {esser2015CAMSAPrsa,
	title = {Resolving scaling ambiguities with the $\ell_1/\ell_2$ norm in a blind deconvolution problem with feedback},
	booktitle = {IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing},
	year = {2015},
	note = {(IEEE CAMSAP Workshop, Canc{\'u}n, Mexico)},
	month = {12},
	pages = {365-368},
	abstract = {Compared to more mundane blind deconvolution problems, blind deconvolution in seismic applications involves a feedback mechanism related to the free surface. The presence of this feedback mechanism gives us an unique opportunity to remove ambiguities that have plagued blind deconvolution for a long time. While beneficial, this feedback by itself is insufficient to remove the ambiguities even with $\ell_1$ constraints. However, when paired with an $\ell_1/\ell_2$ constraint the feedback allows us to resolve the scaling ambiguity under relatively mild assumptions. Inspired by lifting approaches, we propose to split the sparse signal into positive and negative components and apply an $\ell_1/\ell_2$ constraint to the difference, thereby obtaining a constraint that is easy to implement. Numerical experiments demonstrate robustness to the initialization as well as to noise in the data.},
	keywords = {$\ell_1/\ell_2$, blind deconvolution, CAMSAP, lifting, method of multipliers},
	doi = {10.1109/CAMSAP.2015.7383812},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/CAMSAP/2015/esser2015CAMSAPrsa/esser2015CAMSAPrsa.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/CAMSAP/2015/esser2015CAMSAPrsa/esser2015CAMSAPrsa_poster.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/CAMSAP/2015/esser2015CAMSAPrsa/esser2015CAMSAPrsa_ext.pdf},
	author = {Ernie Esser and Rongrong Wang and Tim T.Y. Lin and Felix J. Herrmann}
}
@conference {wason2014SEGrrt,
	title = {Randomization and repeatability in time-lapse marine acquisition},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2014},
	note = {(SEG)},
	month = {10},
	pages = {46-51},
	abstract = {We present an extension of our time-jittered simultaneous marine acquisition to time-lapse surveys where the requirement for repeatability in acquisition can be waived provided we know the acquisition geometry afterwards. Our method, which does not require repetition, gives 4-D signals comparable to conventional methods where repeatability is key to their success.},
	keywords = {Acquisition, deblending, marine, SEG, time-laspe},
	doi = {http://dx.doi.org/10.1190/segam2014-1677.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/wason2014SEGrrt/wason2014SEGrrt.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/wason2014SEGrrt/wason2014SEGrrt_pres.pdf},
	author = {Haneet Wason and Felix Oghenekohwo and Felix J. Herrmann}
}
@conference {herrmann2014EAGEWSrrt,
	title = {Randomization and repeatability in time-lapse marine acquisition},
	booktitle = {EAGE Workshop on Land and Ocean Bottom; Broadband Full Azimuth Seismic Surveys; Spain},
	year = {2014},
	note = {(EAGE Workshop, Spain)},
	month = {04},
	keywords = {4D seismic, EAGE, Marine acquisition, workshop},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/herrmann2014EAGEWSrrt.pdf},
	author = {Haneet Wason and Felix Oghenekohwo and Felix J. Herrmann}
}
@conference {miao2014SEGrhss,
	title = {Randomized HSS acceleration for full-wave-equation depth stepping migration},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2014},
	note = {(SEG)},
	month = {10},
	pages = {3752-3756},
	abstract = {In this work we propose to use the spectral projector (Kenney and Laub, 1995) and randomized HSS technique (Chandrasekaran et al., 2006) to achieve a stable and affordable two-way wave equation depth stepping migration algorithm.},
	keywords = {acoustic, depth extrapolation, full wave equation migration, randomized SVD, SEG, spectral projector},
	doi = {http://dx.doi.org/10.1190/segam2014-1417.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/miao2014SEGrhss/miao2014SEGrhss.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/miao2014SEGrhss/miao2014SEGrhss_pres.pdf},
	author = {Lina Miao and Polina Zheglova and Felix J. Herrmann}
}
@conference {oghenekohwo2014SEGrsw,
	title = {Randomized sampling without repetition in time-lapse surveys},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2014},
	note = {(SEG)},
	month = {10},
	pages = {4848-4852},
	abstract = {Vouching for higher levels of repeatability in acquisition and processing of time-lapse (4D) seismic data has become the standard with oil and gas contractor companies, with significant investment in the design of acquisition systems and processing algorithms that attempt to address some of the current 4D challenges, in particular, imaging weak 4D signals. Recent developments from the field of compressive sensing have shown the benefits of variants of randomized sampling in marine seismic acquisition and its impact for the future of seismic exploration. Following these developments, we show that the requirement for accurate survey repetition in time-lapse seismic data acquisition can be waived provided we solve a sparsity-promoting convex optimization program that makes use of the shared component between the baseline and monitor data. By setting up a framework for inversion of the stacked sections of a time-lapse data, given the pre-stack data volumes, we are able to extract 4D signals with relatively highfidelity from significant subsamplings. Our formulation is applied to time-lapse data that has been acquired with different source/receiver geometries, paving the way for an efficient approach to dealing with time-lapse data acquired with initially poor repeatability levels, provided the survey geometry details are known afterwards.},
	keywords = {4D, Acquisition, random, repetition, SEG, time-lapse},
	doi = {http://dx.doi.org/10.1190/segam2014-1627.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/oghenekohwo2014SEGrsw/oghenekohwo2014SEGrsw.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/oghenekohwo2014SEGrsw/oghenekohwo2014SEGrsw_pres.pdf},
	author = {Felix Oghenekohwo and Rajiv Kumar and Felix J. Herrmann}
}
@conference {herrmann2014ROSErpe,
	title = {Relax the physics and expand the search space {\textendash} FWI via Wavefield Reconstruction Inversion},
	booktitle = {ROSE Consortium; Norway},
	year = {2014},
	note = {(ROSE Consortium)},
	month = {05},
	keywords = {Consortium, FWI, ROSE, WRI},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ROSE/2014/herrmann2014ROSErpe.pdf},
	author = {Felix J. Herrmann}
}
@conference {Herrmann13NIPSrse,
	title = {Randomized sampling in exploration seismology},
	booktitle = {NIPS},
	year = {2013},
	url = {http://techtalks.tv/talks/randomized-sampling-in-exploration-seismology/57871/},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/NIPS/2013/Herrmann13NIPSrse/Herrmann13NIPSrse.pdf},
	author = {Felix J. Herrmann}
}
@conference {herrmann2013SPIErse,
	title = {Randomized sampling in exploration seismology},
	booktitle = {SPIE Optics and Photonics: Wavelets and Sparsity XV},
	year = {2013},
	month = {08},
	keywords = {Exploration seismology, randomized sampling, SPIE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SPIE/2013/herrmann2013SPIErse/herrmann2013SPIErse_pres.pdf},
	author = {Felix J. Herrmann}
}
@conference {herrmann2013KAUSTrse,
	title = {Randomized sampling in exploration seismology},
	booktitle = {KAUST},
	year = {2013},
	month = {05},
	publisher = {KAUST},
	organization = {KAUST},
	keywords = {Exploration seismology, KAUST, randomized sampling},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/KAUST/2013/herrmann2013KAUSTrse/herrmann2013KAUSTrse_pres.pdf},
	author = {Felix J. Herrmann}
}
@conference {herrmann2013SEGOMANrdw,
	title = {Recent developments in wave-equation based inversion technology},
	booktitle = {SEG Workshop on FWI; Oman},
	year = {2013},
	month = {04},
	keywords = {3D, Exploration seismology, FWI, randomized sampling, SEG, workshop},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/herrmann2013SEGOMANrdw/herrmann2013SEGOMANrdw_pres.pdf},
	author = {Felix J. Herrmann}
}
@conference {kumar2013SEGHSS,
	title = {Reconstruction of seismic wavefields via low-rank matrix factorization in the hierarchical-separable matrix representation},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {32},
	year = {2013},
	month = {09},
	pages = {3628-3633},
	abstract = {Recent developments in matrix rank optimization have allowed for new computational approaches in the field of seismic data interpolation. In this paper, we propose an approach for seismic data interpolation which incorporates the Hierarchical Semi-Separable Structure (HSS) inside rank-regularized least-squares formulations for the missing-trace interpolation problem. The proposed approach is suitable for large scale problems, since it avoids SVD computations and uses a low-rank factorized formulation instead. We illustrate the advantages of the new HSS approach by interpolating a seismic line from the Gulf of Suez and compare the reconstruction with conventional rank minimization.},
	keywords = {HSS, interpolation, SEG},
	doi = {10.1190/segam2013-1165.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/kumar2013SEGHSS/kumar2013SEGHSS.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/kumar2013SEGHSS/kumar2013SEGHSS_pres.pdf},
	author = {Rajiv Kumar and Hassan Mansour and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@conference {min2012CSEGrgfe,
	title = {Re-establishment of gradient in frequency-domain elastic waveform inversion},
	booktitle = {CSEG Annual Conference Proceedings},
	year = {2012},
	month = {02},
	abstract = {To obtain solutions close to global minimum in waveform inversion, the gradients computed at each frequency need to be weighted to appropriately describe the residuals between modeled and field data. While the low-frequency components of the gradients should be weighted to recover the long-wavelength structures, the high-frequency components of the gradients need to be weighted when the short-wavelength structures are restored. However, the conventional elastic waveform inversion algorithms cannot properly weight the gradients computed at each frequency. When gradients are scaled using the pseudo-Hessian matrix inside the frequency loop, gradients obtained at high frequencies are over-emphasized. When the gradients are scaled outside the frequency loop, gradients are weighted by the source spectra. In this study, we propose applying weighting factors to the gradients obtained at each frequency so that gradients can properly reflect the differences between the true and assumed models satisfying the general inverse theory. The weighting factors are composed by the backpropagated residuals. Numerical examples for the simple rectangular-shaped model and the modified version of the Marmousi-2 model show that the weighting method enhances gradient images and inversion results compared to the conventional inversion algorithms.},
	keywords = {elastic, frequency-domain, waveform inversion, weighting factors},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/CSEG/2012/min2012CSEGrgfe/min2012CSEGrgfe.pdf},
	author = {Ju-Won Oh and Dong-Joo Min and Felix J. Herrmann}
}
@conference {aravkin2012ICASSProbustb,
	title = {Robust inversion via semistochastic dimensionality reduction},
	booktitle = {ICASSP},
	year = {2012},
	pages = {5245-5248},
	publisher = {ICASSP},
	organization = {ICASSP},
	abstract = {We consider a class of inverse problems where it is possible to aggregate the results of multiple experiments. This class includes problems where the forward model is the solution operator to linear ODEs or PDEs. The tremendous size of such problems motivates the use dimensionality reduction (DR) techniques based on randomly mixing experiments. These techniques break down, however, when robust data-fitting formulations are used, which are essential in cases of missing data, unusually large errors, and systematic features in the data unexplained by the forward model. We survey robust methods within a statistical framework, and propose a sampling optimization approach that allows DR. The efficacy of the methods are demonstrated for a large-scale seismic inverse problem using the robust Student{\textquoteright}s t-distribution, where a useful synthetic velocity model is recovered in the extreme scenario of 60\% corrupted data. The sampling approach achieves this recovery using 20\% of the effort required by a direct robust approach.},
	keywords = {ICASSP},
	doi = {10.1109/ICASSP.2012.6289103},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICASSP/2012/AravkinFriedlanderLeeuwen/AravkinFriedlanderLeeuwen.pdf},
	author = {Aleksandr Y. Aravkin and Michael P. Friedlander and Tristan van Leeuwen}
}
@conference {aravkin2011SEGrobust,
	title = {Robust full-waveform inversion using the Student{\textquoteright}s t-distribution},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {30},
	year = {2011},
	month = {09},
	pages = {2669-2673},
	publisher = {SEG},
	organization = {SEG},
	abstract = {Full-waveform inversion (FWI) is a computational procedure to extract medium parameters from seismic data. Robust methods for FWI are needed to overcome sensitivity to noise and in cases where modeling is particularly poor or far from the real data generating process. We survey previous robust methods from a statistical perspective, and use this perspective to derive a new robust method by assuming the random errors in our model arise from the Student{\textquoteright}s t-distribution. We show that in contrast to previous robust methods, the new method progres- sively down-weighs large outliers, effectively ignoring them once they are large enough. This suggests that the new method is more robust and suitable for situations with very poor data quality or modeling. Experiments show that the new method recovers as well or better than previous robust methods, and can recover models with quality comparable to standard methods on noise-free data when some of the data is completely corrupted, and even when a marine acquisition mask is entirely ignored in the modeling. The ability to ignore a marine acquisition mask via robust FWI methods offers an opportunity for stochastic optimization methods in marine acquisition.},
	keywords = {Full-waveform inversion, Optimization, SEG},
	doi = {10.1190/1.3627747},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2011/aravkin11SEGrobust/aravkin11SEGrobust.pdf},
	author = {Aleksandr Y. Aravkin and Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {aravkin2011ICIAMrfwiu,
	title = {Robust FWI using Student{\textquoteright}s t-distribution},
	booktitle = {ICIAM},
	year = {2011},
	month = {07},
	publisher = {ICIAM 2011},
	organization = {ICIAM 2011},
	abstract = {Iterative inversion algorithms require repeated simulation of 3D time-dependent acoustic, elastic, or electromagnetic wave fields, extending hundreds of wavelengths and hundreds of periods. Also, seismic data is rich in information at every representable scale. Thus simulation-driven optimization approaches to inversion impose great demands on simulator efficiency and accuracy. While computer hardware advances have been of critical importance in bringing inversion closer to practical application, algorithmic advances in simulator methodology have been equally important. Speakers in this two-part session will address a variety of numerical issues arising in the wave simulation, and in its application to inversion.},
	keywords = {Full-waveform inversion, ICIAM, Optimization, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICIAM/2011/aravkin2011ICIAMrfwiu/aravkin2011ICIAMrfwiu.pdf},
	author = {Aleksandr Y. Aravkin and Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {lin2011SEGrssde,
	title = {Robust source signature deconvolution and the estimation of primaries by sparse inversion},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {30},
	year = {2011},
	month = {09},
	pages = {4354-4359},
	publisher = {Dept. of Earth and Ocean Sciences, University of British Columbia},
	organization = {Dept. of Earth and Ocean Sciences, University of British Columbia},
	abstract = {The past few years had seen some concentrated interest on a particular wavefield-inversion approach to the popular SRME multiple removal technique called Estimation of Primaries by Sparse Inversion (EPSI). EPSI promises greatly improved tolerance to noise, missing data, edge effect, and other physi- cal phenomenon generally not described by the SRME relation (van Groenestijn and Verschuur, 2009a,b). It is based on the premise that it is possible to stably invert for both the primary impulse response and the source signature despite beforehand having no (or very limited) explicit knowledge of latter. The key to successful applications of EPSI, as shown in very recent works (Savels et al., 2010), is a robust way to reconstruct very sparse primary impulse response events as part of the inversion process. Based on the various successful demonstrations in literature, there is a very strong sense that EPSI will also play an important role in future developments of source sig- nature deconvolution and the general recovering of wavefield spectrum.},
	keywords = {deconvolution, Presentation, Processing, SEG, sparse inversion},
	doi = {10.1190/1.3628116},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2011/lin11SEGrssde/lin11SEGrssde.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2011/lin11SEGrssde/lin11SEGrssde_pres.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@conference {herrmann2010EAGErds,
	title = {Randomized dimensionality reduction for full-waveform inversion},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2010},
	month = {06},
	abstract = {Full-waveform inversion relies on the collection of large multi-experiment data volumes in combination with a sophisticated back-end to create high-fidelity inversion results. While improvements in acquisition and inversion have been extremely successful, the current trend of incessantly pushing for higher quality models in increasingly complicated regions of the Earth continues to reveal fundamental shortcomings in our ability to handle the ever increasing problem size numerically. Two causes can be identified as the main culprits responsible for this barrier. First, there is the so-called {\textquoteleft}{\textquoteleft}curse of dimensionality{\textquoteright}{\textquoteright} exemplified by Nyquist{\textquoteright}s sampling criterion, which puts disproportionate strain on current acquisition and processing systems as the size and desired resolution of our survey areas continues to increase. Secondly, there is the recent {\textquoteleft}{\textquoteleft}departure from Moore{\textquoteright}s law{\textquoteright}{\textquoteright} that forces us to lower our expectations to compute ourselves out of this. In this paper, we address this situation by randomized dimensionality reduction, which we adapt from the field of compressive sensing. In this approach, we combine deliberate randomized subsampling with structure-exploiting transform-domain sparsity promotion. Our approach is successful because it reduces the size of seismic data volumes without loss of information. With this reduction, we compute Newton-like updates at the cost of roughly one gradient update for the fully-sampled wavefield.},
	keywords = {EAGE, Presentation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2010/herrmann10EAGErds/herrmann10EAGErds.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2010/herrmann10EAGErds/herrmann10EAGErds_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=39352},
	author = {Felix J. Herrmann and Xiang Li}
}
@conference {moghaddam2010SEGrfw,
	title = {Randomized full-waveform inversion: a dimenstionality-reduction approach},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {29},
	year = {2010},
	month = {10},
	pages = {977-982},
	publisher = {SEG},
	organization = {SEG},
	abstract = {Full-waveform inversion relies on the collection of large multi-experiment data volumes in combination with a sophisticated back-end to create high-fidelity inversion results. While improvements in acquisition and inversion have been extremely successful, the current trend of incessantly pushing for higher quality models in increasingly complicated regions of the Earth reveals fundamental shortcomings in our ability to handle increasing problem sizes numerically. Two main culprits can be identified. First, there is the so-called {\textquoteleft}{\textquoteleft}curse of dimensionality{\textquoteright}{\textquoteright} exemplified by Nyquist{\textquoteright}s sampling criterion, which puts disproportionate strain on current acquisition and processing systems as the size and desired resolution increases. Secondly, there is the recent {\textquoteleft}{\textquoteleft}departure from Moore{\textquoteright}s law{\textquoteright}{\textquoteright} that forces us to develop algorithms that are amenable to parallelization. In this paper, we discuss different strategies that address these issues via randomized dimensionality reduction.},
	keywords = {Full-waveform inversion, Optimization, Presentation, SEG},
	doi = {10.1190/1.3513940},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2010/moghaddam10SEGrfw/moghaddam10SEGrfw.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2010/moghaddam10SEGrfw/moghaddam10SEGrfw_pres.pdf},
	author = {Peyman P. Moghaddam and Felix J. Herrmann}
}
@conference {herrmann2010EAGErss,
	title = {Randomized sampling strategies},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2010},
	month = {06},
	abstract = {Seismic exploration relies on the collection of massive data volumes that are subsequently mined for information during seismic processing. While this approach has been extremely successful in the past, the current trend towards higher quality images in increasingly complicated regions continues to reveal fundamental shortcomings in our workflows for high-dimensional data volumes. Two causes can be identified. First, there is the so-called {\textquoteleft}{\textquoteleft}curse of dimensionality{\textquoteright}{\textquoteright} exemplified by Nyquist{\textquoteright}s sampling criterion, which puts disproportionate strain on current acquisition and processing systems as the size and desired resolution of our survey areas continues to increase. Secondly, there is the recent {\textquoteleft}{\textquoteleft}departure from Moore{\textquoteright}s law{\textquoteright}{\textquoteright} that forces us to lower our expectations to compute ourselves out of this curse of dimensionality. In this paper, we offer a way out of this situation by a deliberate randomized subsampling combined with structure-exploiting transform-domain sparsity promotion. Our approach is successful because it reduces the size of seismic data volumes without loss of information. As such we end up with a new technology where the costs of acquisition and processing are no longer dictated by the size of the acquisition but by the transform-domain sparsity of the end-product.},
	keywords = {EAGE, Presentation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2010/herrmann10EAGErss/herrmann10EAGErss.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2010/herrmann10EAGErss/herrmann10EAGErss_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=39131},
	author = {Felix J. Herrmann}
}
@conference {lin2009DELPHIrwi,
	title = {Randomized wavefield inversion},
	booktitle = {DELPHI},
	year = {2009},
	note = {Presented at the DELPHI meeting. The Hague},
	keywords = {Presentation},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/Delphi/2009/lin2009DELPHIrwi/lin2009DELPHIrwi.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann and Yogi A. Erlangga}
}
@conference {herrmann2009SEGrpl,
	title = {Reflector-preserved lithological upscaling},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {28},
	year = {2009},
	month = {10},
	pages = {3466-3470},
	publisher = {SEG},
	organization = {SEG},
	abstract = {By combining Percolation models with lithological smoothing, we arrive at method for upscaling rock elastic constants that preserves reflections. In this approach, the Percolation model predicts sharp onsets in the elastic moduli of sand-shale mixtures when the shales reach a critical volume fraction. At that point, the shale inclusions form a connected cluster, and the macroscopic rock properties change with the power-law growth of the cluster. This switch-like nonlinearity preserves singularities, and hence reflections, even if no sharp transition exists in the lithology or if they are smoothed out using standard upscaling procedures.},
	keywords = {Presentation, SEG},
	doi = {10.1190/1.3255582},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2009/herrmann09SEGrpl/herrmann09SEGrpl.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2009/herrmann09SEGrpl/herrmann09SEGrpl_pres.pdf},
	author = {Felix J. Herrmann}
}
@conference {wang2008SINBADrri,
	title = {Recent results in curvelet-based primary-multiple separation},
	booktitle = {SINBAD 2008},
	year = {2008},
	abstract = {We present a nonlinear curvelet-based sparsity-promoting formulation for the primary-multiple separation problem. We show that these coherent signal components can be separated robustly by explicitly exploiting the locality of curvelets in phase space (space-spatial frequency plane) and their ability to compress data volumes that contain wavefronts. This work is an extension of earlier results and the presented algorithms are shown to be stable under noise and moderately erroneous multiple predictions.},
	keywords = {Presentation, SINBAD, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2008/wang2008SINBADrri/wang2008SINBADrri.pdf},
	author = {Deli Wang and Rayan Saab and Ozgur Yilmaz and Felix J. Herrmann}
}
@conference {moghaddam2008SINBADrtm,
	title = {Reverse-time migration amplitude recovery with curvelets},
	booktitle = {SINBAD 2008},
	year = {2008},
	abstract = {We recover the amplitude of a seismic image by approximating the normal (demigration-migration) operator. In this approximation, we make use of the property that curvelets remain invariant under the action of the normal operator. We propose a seismic amplitude recovery method that employs an eigenvalue like decomposition for the normal operator using curvelets as eigenvectors. Subsequently, we propose an approximate nonlinear singularity-preserving solution to the least-squares seismic imaging problem with sparseness in the curvelet domain and spatial continuity constraints. Our method is tested with a reverse-time {\textquoteright}wave-equation{\textquoteright} migration code simulating the acoustic wave equation.},
	keywords = {Presentation, SINBAD, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2008/moghaddam2008SINBADrtm/moghaddam2008SINBADrtm.pdf},
	author = {Peyman P. Moghaddam}
}
@conference {hennenfent2007SEGrsn,
	title = {Random sampling: new insights into the reconstruction of coarsely sampled wavefields},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2007},
	pages = {2575-2579},
	publisher = {SEG},
	organization = {SEG},
	abstract = {In this paper, we turn the interpolation problem of coarsely-sampled data into a denoising problem. From this point of view, we illustrate the benefit of random sampling at sub-Nyquist rate over regular sampling at the same rate. We show that, using nonlinear sparsity-promoting optimization, coarse random sampling may actually lead to significantly better wavefield reconstruction than equivalent regularly sampled data. \copyright2007 Society of Exploration Geophysicists},
	keywords = {Presentation, SEG, SLIM},
	doi = {10.1190/1.2793002},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/hennenfent07SEGrsn/hennenfent07SEGrsn.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/hennenfent07SEGrsn/hennenfent07SEGrsn_pres.pdf},
	author = {Gilles Hennenfent and Felix J. Herrmann}
}
@conference {herrmann2007EAGErdi,
	title = {Recent developments in curvelet-based seismic processing},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2007},
	month = {06},
	abstract = {Combinations of parsimonious signal representations with nonlinear sparsity promoting programs hold the key to the next-generation of seismic data processing algorithms, since they allow for a formulation that is stable w.r.t. noise \& incomplete data do not require prior information on the velocity or locations and dips of the events},
	keywords = {EAGE, Presentation, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2007/herrmann07EAGErdi/herrmann07EAGErdi.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2007/herrmann07EAGErdi/herrmann07EAGErdi_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=7548},
	author = {Felix J. Herrmann}
}
@conference {herrmann2007SINBADrdi2,
	title = {Recent developments in primary-multiple separation},
	booktitle = {SINBAD 2007},
	year = {2007},
	abstract = {In this talk, we present a novel primary-multiple separation scheme which makes use of the sparsity of both primaries and multiples in a transform domain, such as the curvelet transform, to provide estimates of each. The proposed algorithm utilizes seismic data as well as the output of a preliminary step that provides (possibly) erroneous predictions of the multiples. The algorithm separates the signal components, i.e., the primaries and multiples, by solving an optimization problem that assumes noisy input data and can be derived from a Bayesian perspective. More precisely, the optimization problem can be arrived at via an assumption of a weighted Laplacian distribution for the primary and multiple coefficients in the transform domain and of white Gaussian noise contaminating both the seismic data and the preliminary prediction of the multiples, which both serve as input to the algorithm. Time permitted, we will also briefly discuss a propasal for adaptive curvelet-domain matched filtering. This is joint work with Deli Wang, Rayan Saaba, {\o}zgur Yilmaz and Eric Verschuur.},
	keywords = {Presentation, SINBAD, SLIM},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2007/herrmann07SINBADrdi2/herrmann07SINBADrdi2_pres.pdf},
	author = {Felix J. Herrmann}
}
@conference {hennenfent2007SINBADrii,
	title = {Recent insights in $\ell_1$ solvers},
	booktitle = {SINBAD 2007},
	year = {2007},
	abstract = {During this talk, an overview is given on our work on norm-one solvers as part of the DNOISE project. Gilles will explain the ins and outs of our iterative thresholding solver based on log cooling while Felix will present the work of Michael Friedlander "A Newton root-finding algorithms for large-scale basis pursuit denoise". Both approaches involve the solution of the basis pursuit problem that seeks a minimum one-norm solution of an underdetermined least-squares problem. Basis pursuit denoise (BPDN) fits the least-squares problem only approximately, and a single parameter determines a curve that traces the trade-off between the least-squares fit and the one-norm of the solution. In the work of Friedlander, it is shown show that the function that describes this curve is convex and continuously differentiable over all points of interest. They describe an efficient procedure for evaluating this function and its derivatives. As a result, they can compute arbitrary points on this curve. Their method is suitable for large-scale problems. Only matrix-vector operations are required. This is joint work with Ewout van der Berg and Michael P. Friedlander},
	keywords = {Presentation, SINBAD, SLIM},
	author = {Gilles Hennenfent and Felix J. Herrmann}
}
@conference {wang2007SEGrri,
	title = {Recent results in curvelet-based primary-multiple separation: application to real data},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {26},
	year = {2007},
	pages = {2500-2504},
	publisher = {SEG},
	organization = {SEG},
	abstract = {In this abstract, we present a nonlinear curvelet-based sparsity-promoting formulation for the primary-multiple separation problem. We show that these coherent signal components can be separated robustly by explicitly exploting the locality of curvelets in phase space (space-spatial frequency plane) and their ability to compress data volumes that contain wavefronts. This work is an extension of earlier results and the presented algorithms are shown to be stable under noise and moderately erroneous multiple predictions. \copyright2007 Society of Exploration Geophysicists},
	keywords = {Presentation, SEG, SLIM},
	doi = {10.1190/1.2792986},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/wang07SEGrri/wang07SEGrri.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/wang07SEGrri/wang07SEGrri_pres.pdf},
	author = {Deli Wang and Rayan Saab and Ozgur Yilmaz and Felix J. Herrmann}
}
@conference {fomel2007ICASSPrepro,
	title = {Reproducible computational experiments using scons},
	booktitle = {ICASSP},
	year = {2007},
	publisher = {ICASSP},
	organization = {ICASSP},
	abstract = {SCons (from Software Construction) is a well-known open- source program designed primarily for building software. In this paper, we describe our method of extending SCons for managing data processing flows and reproducible computational experiments. We demonstrate our usage of SCons with a simple example.},
	keywords = {ICASSP},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICASSP/2007/fomel07ICASSPrepro/fomel07ICASSPrepro.pdf},
	author = {Sergey Fomel and Gilles Hennenfent}
}
@conference {hennenfent07gradsem,
	title = {Reproducible research in computational (geo)sciences},
	booktitle = {Graduate seminar series},
	year = {2007},
	month = {01},
	publisher = {Graduate Seminar Series},
	organization = {Graduate Seminar Series},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/Misc/hennenfent07gradsem.pdf},
	author = {Gilles Hennenfent}
}
@conference {moghaddam2007SEGrsi,
	title = {Robust seismic-images amplitude recovery using curvelets},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {26},
	year = {2007},
	pages = {2225-2229},
	publisher = {SEG},
	organization = {SEG},
	abstract = {In this paper, we recover the amplitude of a seismic image by approximating the normal (demigration-migration) operator. In this approximation, we make use of the property that curvelets remain invariant under the action of the normal operator. We propose a seismic amplitude recovery method that employs an eigenvalue like decomposition for the normal operator using curvelets as eigen-vectors. Subsequently, we propose an approximate non-linear singularity-preserving solution to the least-squares seismic imaging problem with sparseness in the curvelet domain and spatial continuity constraints. Our method is tested with a reverse-time {\textquoteleft}wave-equation{\textquoteright} migration code simulating the acoustic wave equation on the SEG-AA salt model. \copyright2007 Society of Exploration Geophysicists},
	keywords = {Presentation, SEG, SLIM},
	doi = {10.1190/1.2792928},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/moghaddam07SEGrsi/moghaddam07SEGrsi.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/moghaddam07SEGrsi/moghaddam07SEGrsi_pres.pdf},
	author = {Peyman P. Moghaddam and Felix J. Herrmann and Christiaan C. Stolk}
}
@conference {maysami2006SINBADrro,
	title = {Recent results on seismic deconvolution},
	booktitle = {SINBAD 2006},
	year = {2006},
	abstract = {One of the important steps in seismic imaging is to provide suitable information about boundaries. Sharp variation of physical properties at a layer boundary cause reflection the wavefield. In previous work done by C. M. Dupuis, seismic signal characterization is divided into two steps: detection and estimation. In the detection phase, the goal is to find all singularities in a seismic section regardless of their order and then to categorize the data to different events by windowing each singularity. In the estimation step, we determine the order of singularity more precisely by using a rough estimate based on the detection phase. Traditionally, a redundant dictionary method is employed for the detection part. However, we attempt to instead use a new L1-solver developed by D.L. Donoho: the Stagewise Orthogonal Matching Pursuit (StOMP). It approximates the solution to inverse problems while promoting the sparsity in the solution vector. This algorithm will allow us to experimentally confirm the recent analysis by S. Mallat on spiky deconvolution limits, which imposes a required minimum distance between spikes. This required minimum distance between different spikes is dependent on the number of spikes as well as the width of the chosen source wavelet used in convolution with the train. These results allow for the design of more robust and accurate detection schemes for seismic signal characterization.},
	keywords = {Presentation, SINBAD, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2006/maysami06SINBADrro/maysami06SINBADrro_pres.pdf},
	author = {Mohammad Maysami}
}
@conference {sastry2007SINBADrfu,
	title = {Recovery from unstructured data},
	booktitle = {SINBAD 2006},
	year = {2006},
	keywords = {Presentation, SINBAD, SLIM},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2006/sastry2007SINBADrfu/sastry2007SINBADrfu.pdf},
	author = {Challa S. Sastry and Gilles Hennenfent and Felix J. Herrmann}
}
@conference {hennenfent2006SINBADros,
	title = {Recovery of seismic data: practical considerations},
	booktitle = {SINBAD 2006},
	year = {2006},
	abstract = {We propose a method for seismic data interpolation based on 1) the reformulation of the problem as a stable signal recovery problem and 2) the fact that seismic data is sparsely represented by curvelets. This method does not require information on the seismic velocities. Most importantly, this formulation potentially leads to an explicit recovery condition. We also propose a large-scale problem solver for the l1-regularization minimization involved in the recovery and successfully illustrate the performance of our algorithm on 2D synthetic and real examples.},
	keywords = {Presentation, SINBAD, SLIM},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2006/hennenfent2006SINBADros/hennenfent2006SINBADros.pdf},
	author = {Gilles Hennenfent}
}
@conference {herrmann2005EAGErcd,
	title = {Robust curvelet-domain data continuation with sparseness constraints},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2005},
	month = {06},
	abstract = {A robust data interpolation method using curvelets frames is presented. The advantage of this method is that curvelets arguably provide an optimal sparse representation for solutions of wave equations with smooth coefficients. As such curvelets frames circum- vent {\textendash} besides the assumption of caustic-free data {\textendash} the necessity to make parametric assumptions (e.g. through linear/parabolic Radon or demigration) regarding the shape of events in seismic data. A brief sketch of the theory is provided as well as a number of examples on synthetic and real data.},
	keywords = {EAGE, Presentation, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2005/Herrmann05EAGErcd/Herrmann05EAGErcd.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2005/Herrmann05EAGErcd/Herrmann05EAGErcd.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=1112},
	author = {Felix J. Herrmann and Gilles Hennenfent}
}
@conference {herrmann2005EAGErcd1,
	title = {Robust curvelet-domain primary-multiple separation with sparseness constraints},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2005},
	month = {06},
	abstract = {A non-linear primary-multiple separation method using curvelets frames is presented. The advantage of this method is that curvelets arguably provide an optimal sparse representation for both primaries and multiples. As such curvelets frames are ideal candidates to separate primaries from multiples given inaccurate predictions for these two data components. The method derives its robustness regarding the presence of noise; errors in the prediction and missing data from the curvelet frame{\textquoteright}s ability (i) to represent both signal components with a limited number of multi-scale and directional basis functions; (ii) to separate the components on the basis of differences in location, orientation and scales and (iii) to minimize correlations between the coefficients of the two components. A brief sketch of the theory is provided as well as a number of examples on synthetic and real data.},
	keywords = {EAGE, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2005/Herrmann05EAGErcd1/Herrmann05EAGErcd1.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=1384},
	author = {Felix J. Herrmann and D. J. Verschuur}
}
