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 signalto-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.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:BVAU.2429/452 |
| Date | January 2004 |
| Creators | Herrmann, Felix J., Moghaddam, Peyman P. |
| Publisher | European Association of Geoscientists and Engineers |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | text |
| Rights | Herrmann, Felix J. |
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