Conclusions

I have shown that a 3-D plane-wave prediction filter can be constructed from a pair of two-dimensional filters by using helix transform and a one-dimensional spectral factorization algorithm.

In all the examples, I used analytical finite-difference filters instead of more general prediction-error filters. A similar factorization idea could be applied to 3-D prediction-error filters. However, treating non-stationarity in this case is less straightforward and requires additional care Clapp et al. (1999); Crawley et al. (1998).

3-D plane-wave prediction filters can find many interesting applications in data processing and inversion. An especially promising application is solution steering in tomography-type problems Clapp et al. (1997); Clapp and Biondi (1998).