A stationary 2D PEF and missing data are simultaneously estimated on sparse data where the 2D PEF is never fully on known data. This PEF is estimated using non-linear conjugate gradients. A weight is applied to the residual to use only fitting equations where a prescribed minimum number of the PEF coefficients are on known data. The minimum parameter is then reduced and a new 2D PEF is estimated using the previous PEF as a starting solution. This process is repeated and the 2D PEF is gradually built up. This method is tested on the Madagascar satellite data. Using increasingly sparse data, the sparse 2D PEF compares favorably to the 2D PEF estimated on the dense data even when 67 percent of the data is unknown.