@article {Mansour11TRssma,
	title = {Randomized marine acquisition with compressive sampling matrices},
	journal = {Geophysical Prospecting},
	volume = {60},
	number = {4},
	year = {2012},
	month = {07},
	pages = {648-662},
	abstract = {Seismic data acquisition in marine environments is a costly process that calls for the adoption of simultaneous-source or randomized acquisition - an emerging technology that is stimulating both geophysical research and commercial efforts. Simultaneous marine acquisition calls for the development of a new set of design principles and post-processing tools. In this paper, we discuss the properties of a specific class of randomized simultaneous acquisition matrices and demonstrate that sparsity-promoting recovery improves the quality of reconstructed seismic data volumes. We propose a practical randomized marine acquisition scheme where the sequential sources fire airguns at only randomly time-dithered instances. We demonstrate that the recovery using sparse approximation from random time-dithering with a single source approaches the recovery from simultaneous-source acquisition with multiple sources. Established findings from the field of compressive sensing indicate that the choice of the sparsifying transform that is incoherent with the compressive sampling matrix can significantly impact the reconstruction quality. Leveraging these findings, we then demonstrate that the compressive sampling matrix resulting from our proposed sampling scheme is incoherent with the curvelet transform. The combined measurement matrix exhibits better isometry properties than other transform bases such as a non-localized multidimensional Fourier transform. We illustrate our results with simulations of "ideal" simultaneous-source marine acquisition, which dithers both in time and space, compared with periodic and randomized time-dithering.},
	keywords = {curvelet transform, Fourier, Marine acquisition},
	doi = {10.1111/j.1365-2478.2012.01075.x},
	url = {http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2478.2012.01075.x/abstract},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalProspecting/2012/Mansour11TRssma/Mansour11TRssma.pdf},
	author = {Hassan Mansour and Haneet Wason and Tim T.Y. Lin and Felix J. Herrmann}
}
@article {wang2008GEOPbws,
	title = {Bayesian wavefield separation by transform-domain sparsity promotion},
	journal = {Geophysics},
	volume = {73},
	number = {5},
	year = {2008},
	month = {07},
	pages = {1-6},
	abstract = {Successful removal of coherent noise sources greatly determines the quality of seismic imaging. Major advances were made in this direction, e.g., Surface-Related Multiple Elimination (SRME) and interferometric ground-roll removal. Still, moderate phase, timing, amplitude errors and clutter in the predicted signal components can be detrimental. Adopting a Bayesian approach along with the assumption of approximate curvelet-domain independence of the to-be-separated signal components, we construct an iterative algorithm that takes the predictions produced by for example SRME as input and separates these components in a robust fashion. In addition, the proposed algorithm controls the energy mismatch between the separated and predicted components. Such a control, which was lacking in earlier curvelet-domain formulations, produces improved results for primary-multiple separation on both synthetic and real data.},
	keywords = {curvelet transform, Geophysics, Optimization, Processing, SLIM},
	doi = {10.1190/1.2952571},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/wang08GEObws/wang08GEObws.pdf},
	html_version = {https://slim.gatech.edu/Publications/Public/Journals/2008/wang08TRbss/paper_html/paper.html},
	author = {Deli Wang and Rayan Saab and Ozgur Yilmaz and Felix J. Herrmann}
}
@article {herrmann2008GEOPcbs,
	title = {Curvelet-based seismic data processing: a multiscale and nonlinear approach},
	journal = {Geophysics},
	volume = {73},
	number = {1},
	year = {2008},
	month = {03},
	pages = {A1-A5},
	publisher = {SEG},
	abstract = {Mitigating missing data, multiples, and erroneous migration amplitudes are key factors that determine image quality. Curvelets, little {\textquoteleft}{\textquoteleft}plane waves,{\textquoteright}{\textquoteright} complete with oscillations in one direction and smoothness in the other directions, sparsify a property we leverage explicitly with sparsity promotion. With this principle, we recover seismic data with high fidelity from a small subset (20\%) of randomly selected traces. Similarly, sparsity leads to a natural decorrelation and hence to a robust curvelet-domain primary-multiple separation for North Sea data. Finally, sparsity helps to recover migration amplitudes from noisy data. With these examples, we show that exploiting the curvelet{\textquoteright}s ability to sparsify wavefrontlike features is powerful, and our results are a clear indication of the broad applicability of this transform to exploration seismology. \copyright2008 Society of Exploration Geophysicists},
	keywords = {Acquisition, curvelet transform, Processing, SLIM},
	doi = {10.1190/1.2799517},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/herrmann08GEOcbs/herrmann08GEOcbs.pdf},
	author = {Felix J. Herrmann and Deli Wang and Gilles Hennenfent and Peyman P. Moghaddam}
}
@article {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}
}
@article {tang2008CITEocs,
	title = {Optimized Compressed Sensing for Curvelet-based Seismic Data Reconstruction},
	journal = {CiteSeer},
	year = {2008},
	abstract = {Compressed sensing (CS) or compressive sampling provides a new sampling theory to reduce data acquisition, which says that compressible signals can be exactly reconstructed from highly incomplete sets of measurements. Very recently, the CS has been applied for seismic exploration and started to compact the traditional data acquisition. In this paper, we present an optimized sampling strategy for the CS data acquisition, which leads to better performance by the curvelet sparsity-promoting inversion in comparison with random sampling and jittered sampling scheme. One of motivation is to reduce the mutual coherence between measurement sampling schemes and curvelet sparse transform in the CS framework. The basic idea of our optimization is to directly redistribute the energy in frequency domain making original spectrum easily discriminated from the random noise induced by random undersampling, while offering control on the maximum gap size. Numerical experiments on synthetic and real seismic data show good performances of the proposed optimized CS for seismic data reconstruction.},
	keywords = {curvelet transform, Optimized Compressive Sensing},
	url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.7994},
	url2 = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.154.7994\&rep=rep1\&type=pdf},
	author = {Wen Tang and Jianwei Ma and Felix J. Herrmann}
}
@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}
}
@article {herrmann2008ACHAsac,
	title = {Sparsity- and continuity-promoting seismic image recovery with curvelet frames},
	journal = {Applied and Computational Harmonic Analysis},
	volume = {24},
	number = {2},
	year = {2008},
	month = {03},
	pages = {150-173},
	abstract = {A nonlinear singularity-preserving solution to seismic image recovery with sparseness and continuity constraints is proposed. We observe that curvelets, as a directional frame expansion, lead to sparsity of seismic images and exhibit invariance under the normal operator of the linearized imaging problem. Based on this observation we derive a method for stable recovery of the migration amplitudes from noisy data. The method corrects the amplitudes during a post-processing step after migration, such that the main additional cost is one ap- plication of the normal operator, i.e. a modeling followed by a migration. Asymptotically this normal operator corresponds to a pseudodifferential operator, for which a convenient diagonal approximation in the curvelet domain is derived, including a bound for its error and a method for the estimation of the diagonal from a compound operator consisting of discrete implementations for the scattering operator and its adjoint the migration operator. The solution is formulated as a nonlinear optimization problem where sparsity in the curvelet domain as well as continuity along the imaged reflectors are jointly promoted. To enhance sparsity, the $ell_1$-norm on the curvelet coefficients is minimized, while continuity is promoted by minimizing an anisotropic diffusion norm on the image. The performance of the recovery scheme is evaluated with a time-reversed {\textquoteright}wave-equation{\textquoteright} migration code on synthetic datasets, including the complex SEG/EAGE AA salt model.},
	keywords = {curvelet transform, Imaging, Processing, SLIM},
	doi = {10.1016/j.acha.2007.06.007},
	url = {https://slim.gatech.edu/Publications/Public/Journals/ACHA/2008/herrmann2008ACHAsac/herrmann2008ACHAsac.pdf},
	author = {Felix J. Herrmann and Peyman P. Moghaddam and Christiaan C. Stolk}
}
