Conclusions

I have reviewed the B-spline forward interpolation method and confirmed the observation of Thévenaz et al. (2000) about its superior performance in comparison with other methods of similar cost. Whenever an accurate forward interpolation scheme is desired, B-splines can be an extremely valuable tool. B-spline forward interpolation involves two steps. The first step is recursive filtering, which results in a set of spline coefficients. The second step is a linear spline interpolation operator.

Analyzing the role of B-spline interpolation in data regularization, I have introduced a method of constructing B-spline discrete regularization operators from continuous differential equations.

Simple numerical experiments with B-spline inverse interpolation show that the main advantage of using a more accurate interpolation scheme occurs in an over-determined setting, where B-splines lead to a more accurate model estimates. In an under-determined setting, the B-spline inverse interpolation scheme converges faster at early iterations, but the total computational gain may be insignificant.

I have shown on a simple real data example that inverse B-spline interpolation can be used as an accurate method of data regularization for processing 3-D seismic reflection data.