An unbiased estimator for the ellipticity from image moments
  An unbiased estimator for the ellipticity of an object in a noisy image is
given in terms of the image moments. Three assumptions are made: i) the pixel
noise is normally distributed, although with arbitrary covariance matrix, ii)
the image moments are taken about a fixed centre, and iii) the point-spread
function is known. The relevant combinations of image moments are then jointly
normal and their covariance matrix can be computed. A particular estimator for
the ratio of the means of jointly normal variates is constructed and used to
provide the unbiased estimator for the ellipticity. Furthermore, an unbiased
estimate of the covariance of the new estimator is also given.
