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The core of the filtering method is the PEF that
destroys the coherent noise present in the residual. In order to
accommodate the possible complexity in space and time of the
undesirable events, these filters can have any dimensions thanks to
the helical boundary conditions
Claerbout (1998); Mersereau and Dudgeon (1974). In addition, these filters
can be made non-stationary in any directions
Claerbout and Fomel (2002); Crawley (2000); Margrave (1998). Chapters
and will illustrate these possibilities.
If a noise model is known in advance, a PEF can be estimated from it
and used directly for the inversion of in equation
(). If a noise model is not known in advance,
I propose the following algorithm based on the iterative inversion of
:

- 1.
- Set and .
- 2.
- Iterate until the data residual contains mostly coherent noise.
- 3.
- Estimate a new PEF from the residual.
- 4.
- Set and iterate.
- 5.
- Inspect the residual. If white then stop else reestimate the
PEF from the unweighted residual and go
to (4).

This nonlinear process tries to refine the PEF estimation by
bootstrapping in order to obtain the best possible coherent
noise filter Clapp (2003).
It is also based on the assumption that the coherent noise
will stay in the residual after a certain number of iterations.
Therefore, the residual needs to be closely watched at
each iteration, which requires a certain level of human interpretation.