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.

9/5/2000