Conclusions and Future Work

When making the jump from stationary to non-stationary interpolation, the issue of interpolating large gaps becomes a much more difficult problem. In addition to worrying about the continuity of the estimate, estimating the value of the filter in the hole is also a problem.

Interpolating filter coefficients with a Laplacian or helical derivative clearly is not a viable approach. A method that preserves the filters, such as nearest neighbor interpolation of filter coefficients proves to be more feasible. When that method incorporates prior information in terms of a preferred direction of regularization and interpolation, the result is greatly improved.

In the future, this method can be applied to large gaps in seismic data, where the preferred direction is either radial lines or Snell rays.