Sparsity- and continuity-promoting seismic image recovery with curvelets
Title | Sparsity- and continuity-promoting seismic image recovery with curvelets |
Publication Type | Conference |
Year of Publication | 2006 |
Authors | Felix J. Herrmann |
Conference Name | SINBAD 2006 |
Keywords | Presentation, SINBAD, SLIM |
Abstract | A nonlinear singularity-preserving solution to seismic image recovery with sparseness and continuity constraints is proposed. The method explicitly explores the curvelet transform as a directional frame expansion that, by virtue of its sparsity on seismic images and its invariance under the Hessian of the linearized imaging problem, allows for a stable recovery of the migration amplitudes from noisy data. The method corresponds to a preconditioning that corrects the amplitudes during a post-processing step. The solution is formulated as a nonlinear optimization problem where sparsity in the curvelet domain as well as continuity along the imaged reflectors are jointly promoted. To enhance sparsity, the l1-norm on the curvelet coefficients is minimized while continuity is promoted by minimizing an anisotropic diffusion norm on the image. The performance of the recovery scheme is evaluated with ’wave-equation’ migration code on a synthetic dataset. This is joint work with Peyman Moghaddam. |
Presentation | |
Citation Key | herrmann2006SINBADsac |