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Curvelet-domain preconditioned "wave-equation" depth-migration with sparseness and illumination constraints

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Title: Curvelet-domain preconditioned "wave-equation" depth-migration with sparseness and illumination constraints
Author: Herrmann, Felix J.; Moghaddam, Peyman P.
Subject Keywords curvelet;seismic inverse scattering;sparseness;illumination;least-squares;reflectivity;edge-preserving;diagonalization
Issue Date: 2004
Publicly Available in cIRcle 2008-02-21
Publisher Society of Exploration Geophysicists
Citation: Herrmann, Felix J. Moghaddam, Peyman. 2004. Curvelet-domain preconditioned "wave-equation" depth-migration with sparseness and illumination constraints. SEG Expanded Abstracts.
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.
Affiliation: Science, Faculty ofEarth and Ocean Sciences, Department of
URI: http://hdl.handle.net/2429/430
Peer Review Status: Unreviewed
Scholarly Level: Faculty

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