@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 {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}
}
