In this talk, directional frames, known as curvelets, are used to recover
seismic data and images from noisy and incomplete data. Sparsity
and invariance properties of curvelets are exploited to formulate
the recovery by a `1-norm promoting program. It is shown that our
data recovery approach is closely linked to the recent theory of “compressive
sensing” and can be seen as a first step towards a nonlinear
sampling theory for wavefields.
The second problem that will be discussed concerns the recovery
of the amplitudes of seismic images in clutter. There, the invariance
of curvelets is used to approximately invert the Gramm operator of
seismic imaging. In the high-frequency limit, this Gramm matrix corresponds
to a pseudo-differential operator, which is near diagonal in
the curvelet domain.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:BVAU.2429/584 |
| Date | January 2007 |
| Creators | Herrmann, Felix J. |
| 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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