The savings are hardly noticeable for simple test problems, but they can have a direct impact on the mere feasibility of iterative least-square inversion for large-scale (seismic-exploration-size) problems.

In the multidimensional case, recursive filtering is enabled by Claerbout's helix transform. The Wilson-Burg spectral factorization method allows us to construct stable recursive filters. By 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.

In the next chapter, I discuss possible choices of the regularization operator and the preconditioning operator in data regularization problems.

12/28/2000