Interpolation of aliased seismic data in the curvelet domain

We propose a robust interpolation scheme for aliased regularly sampled seismic data that uses the curvelet transform. In a first pass, the curvelet transform is used to compute the curvelet coefficients of the aliased seismic data. The aforementioned coefficients are divided into two groups of scales: alias-free and alias-contaminated scales. The alias-free curvelet coefficients are upscaled to estimate a mask function that is used to constrain the inversion of the aliascontaminated scale coefficients. The mask function is incorporated into the inversion via a minimum norm least squares algorithm that determines the curvelet coefficients of the desired alias free data. Once the alias-free coefficients are determined, the curvelet synthesis operator is used to reconstruct seismograms at new spatial positions. The proposed method can be used to reconstruct both regularly and irregularly sampled seismic data. A synthetic data example is used to illustrate the performance of the proposed curvelet interpolation method.