@conference {johnson2008SINBADsdi,
	title = {Seismic data interpolation with symmetry},
	booktitle = {SINBAD 2008},
	year = {2008},
	abstract = {Due to the physics of reciprocity seismic data sets are symmetric in the source and receiver coordinates. Often seismic data sets are incomplete and the missing data must be interpolated. Typically, missing traces do not occur symmetrically. The purpose of this project is to extend the current formulation for solving the seismic interpolation problems in such a way that they enforce reciprocity. The method decomposes the seismic data volume into symmetric and antisymmetric parts. This decomposition leads to an augmented system of equations for the L1-solver that promotes sparsity in the curvelet domain. Interpolation is carried out on the entire system during which the asymmetric component of the volume is forced to zero, while the symmetric part of the data volume is matched to the measured data.},
	keywords = {Presentation, SINBAD, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2008/johnson2008SINBADsdi/johnson2008SINBADsdi.pdf},
	author = {James Johnson and Gilles Hennenfent}
}
@conference {hennenfent2008SINBADsdw2,
	title = {Simply denoise: wavefield reconstruction via jittered undersampling},
	booktitle = {SINBAD 2008},
	year = {2008},
	abstract = {We present a new discrete undersampling scheme designed to favor wavefield reconstruction by sparsity-promoting inversion with transform elements that are localized in the Fourier domain. Our work is motivated by empirical observations in the seismic community, corroborated by recent results from compressive sampling, which indicate favorable (wavefield) reconstructions from random as opposed to regular undersampling. As predicted by theory, random undersampling renders coherent aliases into harmless incoherent random noise, effectively turning the interpolation problem into a much simpler denoising problem. A practical requirement of wavefield reconstruction with localized sparsifying transforms is the control on the maximum gap size. Unfortunately, random undersampling does not provide such a control and the main purpose of this paper is to introduce a sampling scheme, coined jittered undersampling, that shares the benefits of random sampling, while offering control on the maximum gap size. Our contribution of jittered sub-Nyquist sampling proofs to be key in the formulation of a versatile wavefield sparsity-promoting recovery scheme that follows the principles of compressive sampling. After studying the behavior of the jittered-undersampling scheme in the Fourier domain, its performance is studied for curvelet recovery by sparsity-promoting inversion (CRSI). Our findings on synthetic and real seismic data indicate an improvement of several decibels over recovery from regularly-undersampled data for the same amount of data collected.},
	keywords = {Presentation, SINBAD, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2008/hennenfent2008SINBADsdw2/hennenfent2008SINBADsdw2.pdf},
	author = {Gilles Hennenfent}
}
@conference {hennenfent2007EAGEcrw,
	title = {Curvelet reconstruction with sparsity-promoting inversion: successes and challenges},
	booktitle = {EAGE Workshop on Curvelets, contourlets, seislets, {\textellipsis} in seismic data processing - where are we and where are we going?},
	year = {2007},
	month = {06},
	abstract = {In this overview of the recent Curvelet Reconstruction with Sparsity-promoting Inversion (CRSI) method, we present our latest 2-D and 3-D interpolation results on both synthetic and real datasets. We compare these results to interpolated data using other existing methods. Finally, we discuss the challenges related to sparsity-promoting solvers for the large-scale problems the industry faces.},
	keywords = {EAGE, Presentation, SLIM, workshop},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2007/hennenfent07EAGEcrw/hennenfent07EAGEcrw.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2007/hennenfent07EAGEcrw/hennenfent07EAGEcrw_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=7553},
	author = {Gilles Hennenfent and Felix J. Herrmann}
}
@conference {hennenfent2007EAGEisf,
	title = {Irregular sampling: from aliasing to noise},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2007},
	month = {06},
	abstract = {Seismic data is often irregularly and/or sparsely sampled along spatial coordinates. We show that these acquisition geometries are not necessarily a source of adversity in order to accurately reconstruct adequately-sampled data. We use two examples to illustrate that it may actually be better than equivalent regularly subsampled data. This comment was already made in earlier works by other authors. We explain this behavior by two key observations. Firstly, a noise-free underdetermined problem can be seen as a noisy well-determined problem. Secondly, regularly subsampling creates strong coherent acquisition noise (aliasing) difficult to remove unlike the noise created by irregularly subsampling that is typically weaker and Gaussian-like.},
	keywords = {EAGE, Presentation, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2007/hennenfent07EAGEisf/hennenfent07EAGEisf.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2007/hennenfent07EAGEisf/hennenfent07EAGEisf_pres.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2007/hennenfent07EAGEisf/hennenfent07EAGEisf_WS.pdf},
	author = {Gilles Hennenfent and Felix J. Herrmann}
}
@conference {hennenfent2007SINBADjdn,
	title = {Just denoise: nonlinear recovery from randomly sampled data},
	booktitle = {SINBAD 2007},
	year = {2007},
	abstract = {In this talk, 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.},
	keywords = {Presentation, SINBAD, SLIM},
	author = {Gilles Hennenfent}
}
@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 {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 {herrmann2007SEGsdp,
	title = {Seismic data processing with curvelets: a multiscale and nonlinear approach},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {26},
	year = {2007},
	pages = {2220-2224},
	publisher = {SEG},
	organization = {SEG},
	abstract = {In this abstract, we present a nonlinear curvelet-based sparsity-promoting formulation of a seismic processing flow, consisting of the following steps: seismic data regularization and the restoration of migration amplitudes. We show that the curvelet{\textquoteright}s wavefront detection capability and invariance under the migration-demigration operator lead to a formulation that is stable under noise and missing data. \copyright2007 Society of Exploration Geophysicists},
	keywords = {Presentation, SEG, SLIM},
	doi = {10.1190/1.2792927},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/herrmann07SEGsdp/herrmann07SEGsdp.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/herrmann07SEGsdp/herrmann07SEGsdp_pres.pdf},
	author = {Felix J. Herrmann and Deli Wang and Gilles Hennenfent and Peyman P. Moghaddam}
}
@conference {herrmann2007EAGEsia,
	title = {Seismic imaging and processing with curvelets},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2007},
	month = {06},
	abstract = {In this paper, we present a nonlinear curvelet-based sparsity-promoting formulation for three problems in seismic processing and imaging namely, seismic data regularization from data with large percentages of traces missing; seismic amplitude recovery for sub-salt images obtained by reverse-time migration and primary-multiple separation, given an inaccurate multiple prediction. We argue why these nonlinear formulations are beneficial.},
	keywords = {EAGE, Presentation, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2007/herrmann07EAGEsia/herrmann07EAGEsia.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2007/herrmann07EAGEsia/herrmann07EAGEsia_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=7075},
	author = {Felix J. Herrmann and Gilles Hennenfent and Peyman P. Moghaddam}
}
@conference {hennenfent2006SEGaos,
	title = {Application of stable signal recovery to seismic data interpolation},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2006},
	pages = {2797-2801},
	publisher = {SEG},
	organization = {SEG},
	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 1-regularization minimization involved in the recovery and successfully illustrate the performance of our algorithm on 2D synthetic and real examples. \copyright2006 Society of Exploration Geophysicists},
	keywords = {amplitude, continuity, curvelets, fast transform, interpolation, iterative thresholding, Presentation, regularization minimization, SEG, seismic data, SLIM},
	doi = {10.1190/1.2370105},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2006/hennenfent06SEGaos/hennenfent06SEGaos.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2006/hennenfent06SEGaos/hennenfent06SEGaos_pres.pdf},
	author = {Gilles Hennenfent and Felix J. Herrmann}
}
@conference {hennenfent2006SINBADtnf,
	title = {The Nonuniform Fast Discrete Curvelet Transform (NFDCT)},
	booktitle = {SINBAD 2006},
	year = {2006},
	abstract = {The authors present an extension of the fast discrete curvelet transform (FDCT) to nonuniformly sampled data. This extension not only restores curvelet compression rates for nonuniformly sampled data but also removes noise and maps the data to a regular grid.},
	keywords = {Presentation, SINBAD, SLIM},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2006/hennenfent2006SINBADtnf/hennenfent2006SINBADtnf.pdf},
	author = {Gilles Hennenfent}
}
@conference {hennenfent2006SINBADapo,
	title = {A primer on sparsity transforms: curvelets and wave atoms},
	booktitle = {SINBAD 2006},
	year = {2006},
	abstract = {During this presentation an introduction will be given on the method of stable recovery from noisy and incomplete data. Strong recovery conditions that guarantee the recovery for arbitrary acquisition geometries will be reviewed and numerical recovery examples will be presented.},
	keywords = {Presentation, SINBAD, SLIM},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2006/hennenfent2006SINBADapo/hennenfent2006SINBADapo.pdf},
	author = {Gilles Hennenfent}
}
@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 {herrmann2005CSEGnld,
	title = {Non-linear data continuation with redundant frames},
	booktitle = {CSEG Annual Conference Proceedings},
	year = {2005},
	month = {05},
	publisher = {CSEG},
	organization = {CSEG},
	abstract = {We propose an efficient iterative data interpolation method using continuity along reflectors in seismic images via curvelet and discrete cosine transforms. The curvelet transform is a new multiscale transform that provides sparse representations for images that comprise smooth objects separated by piece-wise smooth discontinuities (e.g. seismic images). The advantage of using curvelets is that these frames are sparse for high-frequency caustic-free solutions of the wave-equation. Since we are dealing with less than ideal data (e.g. bandwidth-limited), we compliment the curvelet frames with the discrete cosine transform. The latter is motivated by the successful data continuation with the discrete Fourier transform. By choosing generic basis functions we circumvent the necessity to make parametric assumptions (e.g., through linear/parabolic Radon or demigration) regarding the shape of events in seismic data. Synthetic and real data examples demonstrate that our algorithm provides interpolated traces that accurately reproduce the wavelet shape as well as the AVO behavior along events in shot gathers.},
	keywords = {Presentation, SLIM},
	url = {http://www.cseg.ca/assets/files/resources/abstracts/2005/101S0201-Herrmann_F_Non_Linear_Data_Continuation.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/CSEG/2005/Herrmann05CSEGnld/Herrmann05CSEGnld_pres.pdf},
	author = {Felix J. Herrmann and 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 {hennenfent2005EAGEsdr,
	title = {Seismic deconvolution revisited with curvelet frames},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2005},
	month = {06},
	abstract = {We propose an efficient iterative curvelet-regularized deconvolution algorithm that exploits continuity along reflectors in seismic images. Curvelets are a new multiscale transform that provides sparse representations for images (such as seismic images) that comprise smooth objects separated by piece-wise smooth discontinuities. Our technique combines conjugate gradient-based convolution operator inversion with noise regularization that is performed using non-linear curvelet coefficient shrinkage (thresholding). The shrinkage operation leverages the sparsity of curvelets representations. Simulations demonstrate that our algorithm provides improved resolution compared to the traditional Wiener-based deconvolution approach.},
	keywords = {EAGE, Presentation, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2005/Hennenfent05EAGEsdr/Hennenfent05EAGEsdr.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2005/Hennenfent05EAGEsdr/Hennenfent05EAGEsdr_poster.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=1383},
	author = {Gilles Hennenfent and R. Neelamani and Felix J. Herrmann}
}
@conference {hennenfent2005SEGscd,
	title = {Sparseness-constrained data continuation with frames: applications to missing traces and aliased signals in 2/3-D},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2005},
	pages = {2162-2165},
	publisher = {SEG},
	organization = {SEG},
	abstract = {We present a robust iterative sparseness-constrained interpolation algorithm using 2-/3-D curvelet frames and Fourier-like transforms that exploits continuity along reflectors in seismic data. By choosing generic transforms, we circumvent the necessity to make parametric assumptions (e.g. through linear/parabolic Radon or demigration) regarding the shape of events in seismic data. Simulation and real data examples for data with moderately sized gaps demonstrate that our algorithm provides interpolated traces that accurately reproduce the wavelet shape as well as the AVO behavior. Our method also shows good results for de-aliasing judged by the behavior of the ($f-k$)-spectrum before and after regularization. \copyright2005 Society of Exploration Geophysicists},
	keywords = {Presentation, SEG, SLIM},
	doi = {10.1190/1.2148142},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2005/Hennenfent05SEGscd/Hennenfent05SEGscd.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2005/Hennenfent05SEGscd/Hennenfent05SEGscd_pres.pdf},
	author = {Gilles Hennenfent and Felix J. Herrmann}
}
@conference {hennenfent2005CSEGscs,
	title = {Sparseness-constrained seismic deconvolution with curvelets},
	booktitle = {CSEG Annual Conference Proceedings},
	year = {2005},
	month = {05},
	publisher = {CSEG},
	organization = {CSEG},
	abstract = {Continuity along reflectors in seismic images is used via Curvelet representation to stabilize the convolution operator inversion. The Curvelet transform is a new multiscale transform that provides sparse representations for images that comprise smooth objects separated by piece-wise smooth discontinuities (e.g. seismic images). Our iterative Curvelet-regularized deconvolution algorithm combines conjugate gradient-based inversion with noise regularization performed using non-linear Curvelet coefficient thresholding. The thresholding operation enhances the sparsity of Curvelet representations. We show on a synthetic example that our algorithm provides improved resolution and continuity along reflectors as well as reduced ringing effect compared to the iterative Wiener-based deconvolution approach.},
	keywords = {Presentation, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/CSEG/2005/Hennenfent05CSEGscs/Hennenfent05CSEGscs.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/CSEG/2005/Hennenfent05CSEGscs/Hennenfent05CSEGscs_pres.pdf},
	author = {Gilles Hennenfent and Felix J. Herrmann and R. Neelamani}
}
@conference {hennenfent2004SEGtta,
	title = {Three-term amplitude-versus-offset (AVO) inversion revisited by curvelet and wavelet transforms},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2004},
	pages = {211-214},
	publisher = {SEG},
	organization = {SEG},
	abstract = {We present a new method to stabilize the three-term AVO inversion using Curvelet and Wavelet transforms. Curvelets are basis functions that effectively represent otherwise smooth objects having discontinuities along smooth curves. The applied formalism explores them to make the most of the continuity along reflectors in seismic images. Combined with Wavelets, Curvelets are used to denoise the data by penalizing high frequencies and small contributions in the AVO-cube. This approach is based on the idea that rapid amplitude changes along the ray-parameter axis are most likely due to noise. The AVO-inverse problem is linearized, formulated and solved for all (x, z) at once. Using densities and velocities of the Marmousi model to define the fluctuations in the elastic properties, the performance of the proposed method is studied and compared with the smoothing along the ray-parameter direction only. We show that our method better approximates the true data after the denoising step, especially when noise level increases. \copyright2004 Society of Exploration Geophysicists},
	keywords = {Presentation, SEG, SLIM},
	doi = {10.1190/1.1851201},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2004/Hennenfent04SEGtta/Hennenfent04SEGtta.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2004/Hennenfent04SEGtta/Hennenfent04SEGtta_pres.pdf},
	author = {Gilles Hennenfent and Felix J. Herrmann}
}
