Two complementary solution strategies to the least-squares migration problem with sparseness- & continuity constraints are proposed. The applied formalism explores the sparseness of curvelets on the reflectivity and their invariance under the demigration migration operator. Sparseness is enhanced by (approximately) minimizing a (weighted) l1-norm on the curvelet coefficients. Continuity along imaged reflectors is brought out by minimizing the anisotropic difussion or total variation norm which penalizes variations along and in between reflectors. A brief sketch of the theory is provided as well as a number of synthetic examples. Technical details on the implementation of the optimization strategies are deferred to an accompanying paper: implementation.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:BVAU.2429/500 |
| Date | January 2005 |
| Creators | Herrmann, Felix J., Moghaddam, Peyman P., Kirlin, Rodney L. |
| Publisher | European Association of Geoscientists & 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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