Short Note
The Burg Method on a Helix?

Jon Claerbout

claerbout@stanford.edu

We have not yet put the Burg method of PEF estimation on a helix. The first reason to do so is that the Burg method assures us a stable PEF. The second reason to do so is that the Burg method should be much faster than conjugate gradients. For data length ND and filter length NF, the PEF estimation costs are

          Conjugate gradients    ND*NF**2
          Levinson               ND*NF + NF**2
          Burg                   ND*NF

Estimating PEF's on a helix with the Burg method does not seem difficult: Terms in sums that involve missing data can simply be omitted from certain averages. We could probably proceed much as we now do with conjugate gradients (CG).

PEF estimation is not our main problem, however. Our main problem is missing data. The Burg method has not yet been adapted to missing data estimation but we should try.

It remains to be seen how we can estimate missing values, both off the ends of the data and internal to it. As with CG, polynomial division seems to be an important part of the solution.