Curvelet imaging and processing: sparseness-constrained least-squares migration

TitleCurvelet imaging and processing: sparseness-constrained least-squares migration
Publication TypeConference
Year of Publication2004
AuthorsFelix J. Herrmann, Peyman P. Moghaddam
Conference NameCSEG Annual Conference Proceedings
KeywordsPresentation, SLIM

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 to the (de)-migration operators, almost diagonalized by the Curvelet transform.

Citation Keyherrmann2004CSEGcia2