The fast generalized Fourier transform (FGFT) algorithm is extended to two-dimensional (2D) data cases. The 2D FGFT algorithm provides a fast and non-redundant alternative for the simultaneous time-frequency and space-wavenumber analysis of the data with time-space dependencies. The transform decomposes the data based on the local slope information, and therefore making it possible to extract weight function based on dominant dips from the alias-free low frequencies. By projecting the extracted weight function to the alias-contaminated high frequencies and utilizing a least-squares fitting algorithm, a beyond-alias interpolation method is accomplished. Synthetic and real data examples are provided to examine the performance of the proposed interpolation method.
View full article as PDF (1.59 Mb)