@article {sanavi2021tad,
	title = {True amplitude depth migration using curvelets},
	journal = {Geophysics},
	volume = {86},
	number = {4},
	year = {2021},
	note = {(Geophysics)},
	month = {07},
	pages = {S299-S310},
	abstract = {We have developed a true amplitude solution to the seismic imaging problem. We derive a diagonal scaling approach for the normal operator approximation in the curvelet domain. This is based on the theorem that states that curvelets remain approximately invariant under the action of the normal operator. We use curvelets as essential tools for approximation and inversion. We also exploit the theorem that states that the curvelet-domain approximation should be smooth in phase space by enforcing the smoothness of curvelet coefficients in the angle and space domains. We analyze our method using a reverse time migration-demigration code, simulating the acoustic wave equation on different synthetic models. Our method produces a good resolution with reflecting dips, reproduces the true amplitude reflectors, and compensates for incomplete illumination in seismic images.},
	keywords = {amplitude, depth migration, Imaging, inversion, LSRTM},
	doi = {10.1190/geo2019-0307.1},
	author = {Hamideh Sanavi and Peyman P. Moghaddam and Felix J. Herrmann}
}
@article {herrmann2009GEOPcbm,
	title = {Curvelet-based migration preconditioning and scaling},
	journal = {Geophysics},
	volume = {74},
	year = {2009},
	month = {07-08},
	pages = {A41-A46},
	abstract = {The extremely large size of typical seismic imaging problems has been one of the major stumbling blocks for iterative techniques to attain accurate migration amplitudes. These iterative methods are important because they complement theoretical approaches that are hampered by difficulties to control problems such as finite-acquisition aperture, source-receiver frequency response, and directivity. To solve these problems, we apply preconditioning, which significantly improves convergence of least-squares migration. We discuss different levels of preconditioning that range from corrections for the order of the migration operator to corrections for spherical spreading, and position and reflector-dip dependent amplitude errors. While the first two corrections correspond to simple scalings in the Fourier and physical domain, the third correction requires phase-space (space spanned by location and dip) scaling, which we carry out with curvelets. We show that our combined preconditioner leads to a significant improvement of the convergence of least-squares {\textquoteleft}wave-equation{\textquoteright} migration on a line from the SEG AA{\textquoteright} salt model.},
	keywords = {Imaging, migration, SLIM},
	doi = {10.1190/1.3124753},
	url = {http://geophysics.geoscienceworld.org/content/74/4/A41.abstract},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2009/herrmann2009GEOPcbm/herrmann2009GEOPcbm.pdf},
	author = {Felix J. Herrmann and Cody R. Brown and Yogi A. Erlangga 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}
}
