Scale and Direction-guided 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 alias-contaminated 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. A real data example is used to illustrate the performance of the proposed curvelet interpolation method.