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Curvelet-domain preconditioned "wave-equation" depth-migration with sparseness and illumination constraints Herrmann, Felix J.; Moghaddam, Peyman P.
Abstract
A non-linear edge-preserving solution to the least-squares migration problem with sparseness & illumination constraints is proposed. The applied formalism explores Curvelets as basis functions. By virtue of their sparseness and locality, Curvelets not only reduce the dimensionality of the imaging problem but they also naturally lead to a dense preconditioning that almost diagonalizes the normal/Hessian operator. This almost diagonalization allows us to recast the imaging problem into a ’simple’ denoising problem. As such, we are in the position to use non-linear estimators based on thresholding. These estimators exploit the sparseness and locality of Curvelets and allow us to compute a first estimate for the reflectivity, which approximates the least-squares solution of the seismic inverse scattering problem. Given this estimate, we impose sparseness and additional amplitude corrections by solving a constrained optimization problem. This optimization problem is initialized and constrained by the thresholded image and is designed to remove remaining imaging artifacts and imperfections in the estimation and reconstruction.
Item Metadata
Title |
Curvelet-domain preconditioned "wave-equation" depth-migration with sparseness and illumination constraints
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Creator | |
Contributor | |
Publisher |
Society of Exploration Geophysicists
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Date Issued |
2004
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Description |
A non-linear edge-preserving solution to the least-squares migration problem with sparseness & illumination constraints is proposed. The applied formalism explores Curvelets as basis functions. By virtue of their sparseness and locality, Curvelets not only reduce the dimensionality of the imaging problem but they also naturally lead to a dense preconditioning that almost diagonalizes the normal/Hessian operator.
This almost diagonalization allows us to recast the imaging problem into a ’simple’ denoising problem. As such, we are in the position to use non-linear estimators based on thresholding. These estimators exploit
the sparseness and locality of Curvelets and allow us to compute a first estimate for the reflectivity, which approximates the least-squares solution of the seismic inverse scattering problem. Given this estimate,
we impose sparseness and additional amplitude corrections by solving a constrained optimization problem. This optimization problem is initialized and constrained by the thresholded image and is designed to remove remaining imaging artifacts and imperfections in the estimation and reconstruction.
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Extent |
747539 bytes
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Subject | |
Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2008-02-21
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Provider |
Vancouver : University of British Columbia Library
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Rights |
All rights reserved
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DOI |
10.14288/1.0107385
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URI | |
Affiliation | |
Citation |
Herrmann, Felix J. Moghaddam, Peyman. 2004. Curvelet-domain preconditioned "wave-equation" depth-migration with sparseness and illumination constraints. SEG Expanded Abstracts.
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Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty; Other
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Aggregated Source Repository |
DSpace
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All rights reserved