@article {hennenfent2010GEOPnct,
	title = {Nonequispaced curvelet transform for seismic data reconstruction: a sparsity-promoting approach},
	journal = {Geophysics},
	volume = {75},
	number = {6},
	year = {2010},
	month = {12},
	pages = {WB203-WB210},
	publisher = {SEG},
	abstract = {We extend our earlier work on the nonequispaced fast discrete curvelet transform (NFDCT) and introduce a second generation of the transform. This new generation differs from the previous one by the approach taken to compute accurate curvelet coefficients from irregularly sampled data. The first generation relies on accurate Fourier coefficients obtained by an l2-regularized inversion of the nonequispaced fast Fourier transform (FFT) whereas the second is based on a direct l1-regularized inversion of the operator that links curvelet coefficients to irregular data. Also, by construction the second generation NFDCT is lossless unlike the first generation NFDCT. This property is particularly attractive for processing irregularly sampled seismic data in the curvelet domain and bringing them back to their irregular record-ing locations with high fidelity. Secondly, we combine the second generation NFDCT with the standard fast discrete curvelet transform (FDCT) to form a new curvelet-based method, coined nonequispaced curvelet reconstruction with sparsity-promoting inversion (NCRSI) for the regularization and interpolation of irregularly sampled data. We demonstrate that for a pure regularization problem the reconstruction is very accurate. The signal-to-reconstruction error ratio in our example is above 40 dB. We also conduct combined interpolation and regularization experiments. The reconstructions for synthetic data are accurate, particularly when the recording locations are optimally jittered. The reconstruction in our real data example shows amplitudes along the main wavefronts smoothly varying with limited acquisition imprint.},
	keywords = {curvelet transforms, data acquisition, geophysical techniques, Processing, seismology, SLIM},
	doi = {10.1190/1.3494032},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2010/hennenfent2010GEOPnct/hennenfent2010GEOPnct.pdf},
	author = {Gilles Hennenfent and Lloyd Fenelon and Felix J. Herrmann}
}
@conference {herrmann09EAGEbnrs,
	title = {Beating Nyquist by randomized sampling},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2009},
	note = {Presented at the EAGE (workshop), Amsterdam},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2009/herrmann09EAGEbnrs/herrmann09EAGEbnrs.pdf},
	author = {Felix J. Herrmann and Gang Tang and Reza Shahidi and Gilles Hennenfent and Tim T.Y. Lin}
}
@article {vandenberg2009ACMstf,
	title = {Sparco: a testing framework for sparse reconstruction},
	journal = {ACM Transactions on Mathematical Software},
	volume = {35},
	number = {4},
	year = {2009},
	month = {02},
	pages = {1-16},
	abstract = {Sparco is a framework for testing and benchmarking algorithms for sparse reconstruction. It includes a large collection of sparse reconstruction problems drawn from the imaging, compressed sensing, and geophysics literature. Sparco is also a framework for implementing new test problems and can be used as a tool for reproducible research. Sparco is implemented entirely in Matlab, and is released as open-source software under the GNU Public License.},
	keywords = {compressed sensing, linear operators, Sparse recovery},
	url = {http://doi.acm.org/10.1145/1462173.1462178},
	author = {Ewout van den Berg and Michael P. Friedlander and Gilles Hennenfent and Felix J. Herrmann and Rayan Saab and Ozgur Yilmaz}
}
@article {herrmann2008GEOPcbs,
	title = {Curvelet-based seismic data processing: a multiscale and nonlinear approach},
	journal = {Geophysics},
	volume = {73},
	number = {1},
	year = {2008},
	month = {03},
	pages = {A1-A5},
	publisher = {SEG},
	abstract = {Mitigating missing data, multiples, and erroneous migration amplitudes are key factors that determine image quality. Curvelets, little {\textquoteleft}{\textquoteleft}plane waves,{\textquoteright}{\textquoteright} complete with oscillations in one direction and smoothness in the other directions, sparsify a property we leverage explicitly with sparsity promotion. With this principle, we recover seismic data with high fidelity from a small subset (20\%) of randomly selected traces. Similarly, sparsity leads to a natural decorrelation and hence to a robust curvelet-domain primary-multiple separation for North Sea data. Finally, sparsity helps to recover migration amplitudes from noisy data. With these examples, we show that exploiting the curvelet{\textquoteright}s ability to sparsify wavefrontlike features is powerful, and our results are a clear indication of the broad applicability of this transform to exploration seismology. \copyright2008 Society of Exploration Geophysicists},
	keywords = {Acquisition, curvelet transform, Processing, SLIM},
	doi = {10.1190/1.2799517},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/herrmann08GEOcbs/herrmann08GEOcbs.pdf},
	author = {Felix J. Herrmann and Deli Wang and Gilles Hennenfent and Peyman P. Moghaddam}
}
@conference {hennenfent2008SINBADnii2,
	title = {New insights into one-norm solvers from the Pareto curve},
	booktitle = {SINBAD},
	year = {2008},
	abstract = {Several geophysical ill-posed inverse problems are successfully solved by promoting sparsity using one-norm regularization. The practicality of this approach depends on the effectiveness of the one-norm solver used and on its robustness under limited number of iterations. We propose an approach to understand the behavior and evaluate the performance of one-norm solvers. The technique consists of tracking on a graph the data misfit versus the one norm of successive iterates. By comparing the solution paths to the Pareto curve, we are able to assess the performance of the solvers and the quality of the solutions. Such an assessment is particularly relevant given the renewed interest in one-norm regularization.},
	keywords = {SINBAD, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2008/hennenfent2008SINBADnii2/hennenfent2008SINBADnii2.pdf},
	author = {Gilles Hennenfent}
}
@article {hennenfent2008GEOPnii,
	title = {New insights into one-norm solvers from the Pareto curve},
	journal = {Geophysics},
	volume = {73},
	number = {4},
	year = {2008},
	month = {07},
	pages = {A23-A26},
	abstract = {Geophysical inverse problems typically involve a trade off between data misfit and some prior. Pareto curves trace the optimal trade off between these two competing aims. These curves are commonly used in problems with two-norm priors where they are plotted on a log-log scale and are known as L-curves. For other priors, such as the sparsity-promoting one norm, Pareto curves remain relatively unexplored. We show how these curves lead to new insights in one-norm regularization. First, we confirm the theoretical properties of smoothness and convexity of these curves from a stylized and a geophysical example. Second, we exploit these crucial properties to approximate the Pareto curve for a large-scale problem. Third, we show how Pareto curves provide an objective criterion to gauge how different one-norm solvers advance towards the solution.},
	keywords = {Acquisition, Geophysics, Optimization, Pareto, Processing, SLIM},
	doi = {10.1190/1.2944169},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/hennenfent08GEOnii/hennenfent08GEOnii.pdf},
	author = {Gilles Hennenfent and Ewout van den Berg and Michael P. Friedlander and Felix J. Herrmann}
}
@article {herrmann2008GJInps,
	title = {Non-parametric seismic data recovery with curvelet frames},
	journal = {Geophysical Journal International},
	volume = {173},
	year = {2008},
	month = {04},
	pages = {233-248},
	abstract = {Seismic data recovery from data with missing traces on otherwise regular acquisition grids forms a crucial step in the seismic processing flow. For instance, unsuccessful recovery leads to imaging artifacts and to erroneous predictions for the multiples, adversely affecting the performance of multiple elimination. A non-parametric transform-based recovery method is presented that exploits the compression of seismic data volumes by recently developed curvelet frames. The elements of this transform are multidimensional and directional and locally resemble wavefronts present in the data, which leads to a compressible representation for seismic data. This compression enables us to formulate a new curvelet-based seismic data recovery algorithm through sparsity-promoting inversion. The concept of sparsity-promoting inversion is in itself not new to geophysics. However, the recent insights from the field of {\textquoteleft}compressed sensing{\textquoteright} are new since they clearly identify the three main ingredients that go into a successful formulation of a recovery problem, namely a sparsifying transform, a sampling strategy that subdues coherent aliases and a sparsity-promoting program that recovers the largest entries of the curvelet-domain vector while explaining the measurements. These concepts are illustrated with a stylized experiment that stresses the importance of the degree of compression by the sparsifying transform. With these findings, a curvelet-based recovery algorithms is developed, which recovers seismic wavefields from seismic data volumes with large percentages of traces missing. During this construction, we benefit from the main three ingredients of compressive sampling, namely the curvelet compression of seismic data, the existence of a favorable sampling scheme and the formulation of a large-scale sparsity-promoting solver based on a cooling method. The recovery performs well on synthetic as well as real data and performs better by virtue of the sparsifying property of curvelets. Our results are applicable to other areas such as global seismology.},
	keywords = {Acquisition, curvelet transform, reconstruction, SLIM},
	doi = {10.1111/j.1365-246X.2007.03698.x},
	url = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalJournalInternational/2008/herrmann2008GJInps.pdf},
	author = {Felix J. Herrmann and Gilles Hennenfent}
}
@techreport {hennenfent08TRori,
	title = {One-norm regularized inversion: learning from the Pareto curve},
	number = {TR-EOAS-2008-5},
	year = {2008},
	institution = {UBC Earth and Ocean Sciences Department},
	abstract = {Geophysical inverse problems typically involve a trade off between data misfit and some prior. Pareto curves trace the optimal trade off between these two competing aims. These curves are commonly used in problems with two-norm priors where they are plotted on a log-log scale and are known as L-curves. For other priors, such as the sparsity-promoting one norm, Pareto curves remain relatively unexplored. First, we show how these curves provide an objective criterion to gauge how robust one-norm solvers are when they are limited by a maximum number of matrix-vector products that they can perform. Second, we use Pareto curves and their properties to define and compute one-norm compressibilities. We argue this notion is key to understand one-norm regularized inversion. Third, we illustrate the correlation between the one-norm compressibility and the performance of Fourier and curvelet reconstructions with sparsity promoting inversion.},
	keywords = {SLIM},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2008/hennenfent08TRori/hennenfent08TRori.pdf},
	author = {Gilles Hennenfent and Felix J. Herrmann}
}
@conference {hennenfent2008SEGonri,
	title = {One-norm regularized inversion: learning from the Pareto curve},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2008},
	publisher = {SEG},
	organization = {SEG},
	abstract = {Geophysical inverse problems typically involve a trade off between data misfit and some prior. Pareto curves trace the optimal trade off between these two competing aims. These curves are commonly used in problems with two-norm priors where they are plotted on a log-log scale and are known as L-curves. For other priors, such as the sparsity-promoting one norm, Pareto curves remain relatively unexplored. First, we show how these curves provide an objective criterion to gauge how robust one-norm solvers are when they are limited by a maximum number of matrix-vector products that they can perform. Second, we use Pareto curves and their properties to define and compute one-norm compressibilities. We argue this notion is key to understand one-norm regularized inversion. Third, we illustrate the correlation between the one-norm compressibility and the perfor- mance of Fourier and curvelet reconstructions with sparsity promoting inversion.},
	keywords = {SEG},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2008/hennenfent08SEGonri/hennenfent08SEGonri.pdf},
	author = {Gilles Hennenfent and Felix J. Herrmann}
}
@manual {hennenfent08MNrap,
	title = {Repro: a Python package for automating reproducible research in scientific computing},
	year = {2008},
	month = {08},
	abstract = {Repro is a Python package for automating reproducible research in scientific computing. Repro works in combination with SCons, a next-generation build tool. The package is freely available over the Internet. Downloading and installation instructions are provided in this gui de. The repro package is documented in various ways (many comments in source code, this guide{\textendash}-written using repro itself!{\textendash}-and a reference guide). In this user{\textquoteright}s guide, we present a few pedagogical examples that uses Matlab, Python, Seismic Unix (SU), and Madagascar. We also include demo pa pers. These papers are written in LaTeX and compiled using repro. The figures they contain are automatically generated from the source codes prov ided. In that sense, the demo papers are a model of self-contained documents that are fully reproducible. The repro package is largely inspired by some parts of Madagascar, a geophysical software package for reproducible research. However, the repro package is intended for a broad audience co ming from a wide spectrum of interest areas.},
	keywords = {SLIM},
	url = {http://repro.sourceforge.net/Site/Home.html},
	author = {Gilles Hennenfent and Sean Ross-Ross}
}
@mastersthesis {hennenfent08phd,
	title = {Sampling and reconstruction of seismic wavefields in the curvelet domain},
	year = {2008},
	note = {(PhD)},
	month = {05},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {Wavefield reconstruction is a crucial step in the seismic processing flow. For instance, unsuccessful interpolation leads to erroneous multiple predictions that adversely affect the performance of multiple elimination, and to imaging artifacts. We present a new non-parametric transform-based reconstruction method that exploits the compression of seismic data by the recently developed curvelet transform. The elements of this transform, called curvelets, are multi-dimensional, multi-scale, and multi-directional. They locally resemble wavefronts present in the data, which leads to a compressible representation for seismic data. This compression enables us to formulate a new curvelet-based seismic data recovery algorithm through sparsity-promoting inversion (CRSI). The concept of sparsity-promoting inversion is in itself not new to geophysics. However, the recent insights from the field of {\textquoteleft}{\textquoteleft}compressed sensing{\textquoteright}{\textquoteright} are new since they clearly identify the three main ingredients that go into a successful formulation of a reconstruction problem, namely a sparsifying transform, a sub-Nyquist sampling strategy that subdues coherent aliases in the sparsifying domain, and a data-consistent sparsity-promoting program. After a brief overview of the curvelet transform and our seismic-oriented extension to the fast discrete curvelet transform, we detail the CRSI formulation and illustrate its performance on synthetic and real datasets. Then, we introduce a sub-Nyquist sampling scheme, termed jittered undersampling, and show that, for the same amount of data acquired, jittered data are best interpolated using CRSI compared to regular or random undersampled data. We also discuss the large-scale one-norm solver involved in CRSI. Finally, we extend CRSI formulation to other geophysical applications and present results on multiple removal and migration-amplitude recovery.},
	keywords = {curvelet transform, reconstruction, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2008/hennenfent08phd.pdf},
	author = {Gilles Hennenfent}
}
@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}
}
@article {hennenfent2008GEOPsdw,
	title = {Simply denoise: wavefield reconstruction via jittered undersampling},
	journal = {Geophysics},
	volume = {73},
	number = {3},
	year = {2008},
	month = {05},
	pages = {V19-V28},
	publisher = {SEG},
	abstract = {In this paper, 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 proves 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 = {Acquisition, Compressive Sensing, Geophysics, Optimization, Processing, sampling, SLIM},
	doi = {10.1190/1.2841038},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/hennenfent08GEOsdw/hennenfent08GEOsdw.pdf},
	html_version = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/hennenfent08GEOsdw/paper_html/paper.html},
	author = {Gilles Hennenfent and Felix J. Herrmann}
}
@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 {yarham2007EAGEcai,
	title = {Curvelet applications in surface wave removal},
	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 = {Ground roll removal of seismic signals can be a challenging prospect. Dealing with undersampleing causing aliased waves amplitudes orders of magnitude higher than reflector signals and low frequency loss of information due to band ...},
	keywords = {EAGE, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2007/yarham07EAGEcai/yarham07EAGEcai.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=7590},
	author = {Carson Yarham and Gilles Hennenfent and Felix J. Herrmann}
}
@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 {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 {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 {challa2007EAGEsrf,
	title = {Signal reconstruction from incomplete and misplaced measurements},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2007},
	month = {06},
	abstract = {Constrained by practical and economical considerations, one often uses seismic data with missing traces. The use of such data results in image artifacts and poor spatial resolution. Sometimes due to practical limitations, measurements may be available on a perturbed grid, instead of on the designated grid. Due to algorithmic requirements, when such measurements are viewed as those on the designated grid, the recovery procedures may result in additional artifacts. This paper interpolates incomplete data onto regular grid via the Fourier domain, using a recently developed greedy algorithm. The basic objective is to study experimentally as to what could be the size of the perturbation in measurement coordinates that allows for the measurements on the perturbed grid to be considered as on the designated grid for faithful recovery. Our experimental work shows that for compressible signals, a uniformly distributed perturbation can be offset with slightly more number of measurements.},
	keywords = {EAGE, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2007/challa07EAGEsrf/challa07EAGEsrf.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=6917},
	author = {Challa S. Sastry and Gilles Hennenfent and Felix J. Herrmann}
}
@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 {hennenfent06SINBADscons,
	title = {Basic Processing flows with SCons},
	booktitle = {SINBAD},
	year = {2006},
	publisher = {SINBAD},
	organization = {SINBAD},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2006/hennenfent06SINBADscons/hennenfent06SINBADscons.pdf},
	author = {Gilles Hennenfent}
}
@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 {thomson2006SEGpwfd,
	title = {A parallel windowed fast discrete curvelet transform applied to seismic processing},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {25},
	year = {2006},
	pages = {2767-2771},
	publisher = {SEG},
	organization = {SEG},
	abstract = {We propose using overlapping, tapered windows to process seismic data in parallel. This method consists of numerically tight linear oper ators and adjoints that are suitable for use in iterative algorithms. This method is also highly scalable and makes parallel processing of large seismic data sets feasible. We use this scheme to define the Parallel Windowed Fast Discrete Curvelet Transform (PWFDCT), which we apply to a seismic data interpolation algorithm. The successful performance of our parallel processing scheme and algorithm on a two-dimensional synthetic data is shown.},
	keywords = {SEG},
	doi = {10.1190/1.2370099},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2006/thomson06SEGpwfd/thomson06SEGpwfd.pdf},
	author = {Darren Thomson and Gilles Hennenfent and Henryk Modzelewski and Felix J. Herrmann}
}
@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 {hennenfent06SINBADssr,
	title = {A primer on stable signal recovery},
	booktitle = {SINBAD},
	year = {2006},
	publisher = {SINBAD},
	organization = {SINBAD},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2006/hennenfent06SINBADssr/hennenfent06SINBADssr.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}
}
@article {hennenfent2006CiSEsdn,
	title = {Seismic denoising with nonuniformly sampled curvelets},
	journal = {Computing in Science \& Engineering},
	volume = {8},
	number = {3},
	year = {2006},
	month = {05},
	pages = {16-25},
	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 = {CiSE, Processing},
	doi = {10.1109/MCSE.2006.49},
	url = {https://slim.gatech.edu/Publications/Public/Journals/CiSE/2006/hennenfent06CiSEsdn/hennenfent06CiSEsdn.pdf},
	author = {Gilles Hennenfent and Felix J. Herrmann}
}
@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}
}
