The fast generalized Fourier transform algorithm is extended to two-dimensional data cases. The algorithm provides a fast and nonredundant alternative for the simultaneous time-frequency and space-wave number 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.