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Now I will summarize our approach to 1-D missing-data restoration
in words that will carry us towards 2-D missing data.
First we noticed that, given a filter,
minimizing the output power will find missing input data
regardless of the volume missing or its geometrical complexity.
Second, we experimented with various filters and saw that
the **prediction-error filter** is an appropriate choice,
because data extensions into regions without data
tend to have the spectrum inverse to the PE filter, which
(from chapter )
is inverse to the known data.
Thus, the overall problem is perceived as a **nonlinear** one,
involving the product of unknown filter coefficients and unknown data.
It is well known
that nonlinear problems are susceptible to multiple solutions;
hence the importance of the stabilization method described,
which enables us to ensure a reasonable solution.
1

** Next:** 2-D interpolation before aliasing
** Up:** MISSING DATA AND UNKNOWN
** Previous:** Spectral preference and training
Stanford Exploration Project

10/21/1998