  We explore the utility of Karhunen Loeve (KL) analysis in solving practical
problems in the analysis of gravitational shear surveys. Shear catalogs from
large-field weak lensing surveys will be subject to many systematic
limitations, notably incomplete coverage and pixel-level masking due to
foreground sources. We develop a method to use two dimensional KL eigenmodes of
shear to interpolate noisy shear measurements across masked regions. We explore
the results of this method with simulated shear catalogs, using statistics of
high-convergence regions in the resulting map. We find that the KL procedure
not only minimizes the bias due to masked regions in the field, it also reduces
spurious peak counts from shape noise by a factor of ~ 3 in the cosmologically
sensitive regime. This indicates that KL reconstructions of masked shear are
not only useful for creating robust convergence maps from masked shear
catalogs, but also offer promise of improved parameter constraints within
studies of shear peak statistics.
