Weak gravitational lensing shear measurement with FPFS: analytical
  mitigation of noise bias and selection bias
  Dedicated 'Stage IV' observatories will soon observe the entire extragalactic
sky, to measure the 'cosmic shear' distortion of galaxy shapes by weak
gravitational lensing. To measure the apparent shapes of those galaxies, we
present an improved version of the Fourier Power Function Shapelets (FPFS)
shear measurement method. This now includes analytic corrections for sources of
bias that plague all shape measurement algorithms: including noise bias (due to
noise in nonlinear combinations of observable quantities) and selection bias
(due to sheared galaxies being more or less likely to be detected). Crucially,
these analytic solutions do not rely on calibration from external image
simulations. For isolated galaxies, the small residual $\sim$$10^{-3}$
multiplicative bias and $\lesssim$$10^{-4}$ additive bias now meet science
requirements for Stage IV experiments. FPFS also works accurately for faint
galaxies and robustly against stellar contamination. Future work will focus on
deblending overlapping galaxies. The code used for this paper can process
$>$$1000$ galaxy images per CPU second and is available from
https://github.com/mr-superonion/FPFS.
