I present an approach to estimate a stationary PEF on sparse data using non-linear conjugate gradients Claerbout (1999) where both the filter and the missing data are estimated simultaneously. I add a weight to use only fitting equations where a prescribed minimum number of filter coefficients are on known data. Then, I reduce the minimum number of filter coefficients and solve again. I repeat this bootstrapping process until all of the data is used. A variant of this method was first suggested by Jon Claerbout and described in Lomask (2002). In this paper, this method proves capable of estimating a 2D PEF on datasets where the known data occurs systematically as in the Madagascar satellite data Curry (2004b); Ecker and Berlioux (1995); Lomask (1998, 2002) or possibly the data used in Curry (2004a). If the data is not too radically non-stationary, this stationary PEF can, in principle, be used as a starting solution for tackling the non-stationary problem.
In the following paper, I first present the methodology for estimating the stationary PEF on sparse data. Then I illustrate its effectiveness on the Madagascar satellite data.