@conference {herrmann2004EAGEcdl, title = {Curvelet-domain least-squares migration with sparseness constraints}, booktitle = {EAGE Annual Conference Proceedings}, year = {2004}, month = {06}, abstract = {A non-linear edge-preserving solution to the least-squares migration problem with sparseness constraints is introduced. The applied formalism explores Curvelets as basis functions that, by virtue of their sparseness and locality, not only allow for a reduction of the dimensionality of the imaging problem but which also naturally lead to a non-linear solution with significantly improved signal-to-noise ratio. Additional conditions on the image are imposed by solving a constrained optimization problem on the estimated Curvelet coefficients initialized by thresholding. This optimization is designed to also restore the amplitudes by (approximately) inverting the normal operator, which is like-wise the (de)-migration operators, almost diagonalized by the Curvelet transform.}, keywords = {EAGE, Presentation, SLIM}, url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2004/Herrmann04EAGEcdl/Herrmann04EAGEcdl.pdf}, presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2004/Herrmann04EAGEcdl/Herrmann04EAGEcdl_pres.pdf}, url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=2073}, author = {Felix J. Herrmann and Peyman P. Moghaddam} }