Conclusions

Applying inverse filtering operators that we can construct with the helix transform to precondition interpolation problems, we observe a significant (order of magnitude) speed-up in the optimization convergence. Since inverse recursive filtering takes almost the same time as forward convolution, the acceleration translates straightforwardly into computational time savings.

For simple test problems, these savings are hardly noticeable. On the other hand, for large-scale (seismic-exploration-size) problems, the achieved acceleration can have a direct impact on the mere feasibility of iterative least-square inversion.