Summary of 1-D missing-data restoration

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.

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