Multidimensional de-aliased Cadzow reconstruction of seismic records

We tested a strategy for beyond-alias interpolation of seismic data using Cadzow reconstruction. The strategy enables Cadzow reconstruction to be used for interpolation of regularly sampled seismic records. First, in the frequency-space (f-x) domain, we generated a Hankel matrix from the spatial samples of the low frequencies. To perform interpolation at a given frequency, the spatial samples were interlaced with zero samples and another Hankel matrix was generated from the zero-interlaced data. Next, the rank-reduced eigen-decomposition of the Hankel matrix at low frequencies was used for beyond-alias preconditioning of the Hankel matrix at a given frequency. Finally, antidiagonal averaging of the conditioned Hankel matrix produced the final interpolated data. In addition, the multidimensional extension of the proposed algorithm was explained. The proposed method provides a unifying thread between reduced-rank Cadzow reconstruction and beyond alias f-x prediction error interpolation. Synthetic and real data examples were provided to examine the performance of the proposed interpolation method.