A non-linear singularity-preserving solution to the least-squares seismic imaging problem with
sparseness and continuity constraints is proposed. The applied formalism explores curvelets as
a directional frame that, by their sparsity on the image, and their invariance under the imaging
operators, allows for a stable recovery of the amplitudes. Our method is based on the estimation
of the normal operator in the form of an ’eigenvalue’ decomposition with curvelets as the
’eigenvectors’. Subsequently, we propose an inversion method that derives from estimation
of the normal operator and is formulated as a convex optimization problem. Sparsity in the
curvelet domain as well as continuity along the reflectors in the image domain are promoted as
part of this optimization. Our method is tested with a reverse-time ’wave-equation’ migration
code simulating the acoustic wave equation.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:BVAU.2429/543 |
| Date | January 2007 |
| Creators | Moghaddam, Peyman P., Herrmann, Felix J., Stolk, Christiaan C. |
| 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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