The Point Spread Function Reconstruction by Using Moffatlets - I
  The shear measurement is a crucial task in the current and the future weak
lensing survey projects. And the reconstruction of the point spread
function(PSF) is one of the essential steps. In this work, we present three
different methods, including Gaussianlets, Moffatlets and EMPCA to quantify
their efficiency on PSF reconstruction using four sets of simulated LSST star
images. Gaussianlets and Moffatlets are two different sets of basis functions
whose profiles are based on Gaussian and Moffat functions respectively.
Expectation Maximization(EM) PCA is a statistical method performing iterative
procedure to find principal components of an ensemble of star images. Our tests
show that: 1) Moffatlets always perform better than Gaussianlets. 2) EMPCA is
more compact and flexible, but the noise existing in the Principal Components
(PCs) will contaminate the size and ellipticity of PSF while Moffatlets keeps
them very well.
