Random Sampling Data Interpolation with Weighted Matching Pursuit (WMP)

Seismic data interpolation can be done by an inverse Fourier transform if the Fourier spectrum of regular and un-aliasing seismic data is well estimated. The pseudo random sampling of the seismic data in time-space, which is based on a regular pattern, yields a F-K spectrum in which the aliasing looks like white noises. Therefore, restoring the F-K spectrum of the regular and non-aliasing data is similar a process of de-noising in F-K domain. A new method which is called WMP is introduced. This method is based on fast MP algorithm with a weighted operator formed with the Radon spectrum of seismic data by assuming that the events are linear. The noise can be removed clearly with the help of the weighted operator, which is proven by numerical examples. The method can be easily extended to high-dimensions.