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A predictionerror filter (PEF) can be estimated by minimizing the following residual,
 
(1) 
where f_{i} are unknown filter values and d_{i} are known data values. In this
case the filter has two free coefficients and there are seven data points. In
practice, the PEF is multidimensional and contains many more coefficients. Once
the PEF has been estimated it can be used in a second leastsquares problem
 

 (2) 
where is a selector matrix which is 1 where data
is present and where it is not, represents convolution with the
PEF and is the desired model. The first line in equation 2
is a hard constraint while the second line is not.
In order for this method to work, the data used as input to equation
1 needs to be similar to the desired output model in equation
2. The slightly different approximations used in tx and fx
PEFs are discussed next.
Next: tx versus fx method
Up: Curry: Nonstationary interpolation in
Previous: Introduction
Stanford Exploration Project
5/6/2007