Imaging operator approximation using curvelets

In this presentation, the normal (demigation-migration) operator is studied in terms of a pseudo-differential operator. The invariance of curvelets under this operator and their sparsity on the seismic images is used to precondition the migration operator. A brief overview will be given on some of the theory from micro-local analysis which proofs that curvelets remain approximately invariant under the operator. The proper setting for which a diagonal approximation in the curvelet domain is accurate is discussed together with different methods that estimate this diagonal from of-the-shelf migration operators. This is joint work with Chris Stolk.