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

An unbiased estimator for the ellipticity from image moments