  We introduce a novel method for weak-lensing measurements, which is based on
a mathematically exact deconvolution of the moments of the apparent brightness
distribution of galaxies from the telescope's PSF. No assumptions on the shape
of the galaxy or the PSF are made. The (de)convolution equations are exact for
unweighted moments only, while in practice a compact weight function needs to
be applied to the noisy images to ensure that the moment measurement yields
significant results. We employ a Gaussian weight function, whose centroid and
ellipticity are iteratively adjusted to match the corresponding quantities of
the source. The change of the moments caused by the application of the weight
function can then be corrected by considering higher-order weighted moments of
the same source. Because of the form of the deconvolution equations, even an
incomplete weighting correction leads to an excellent shear estimation if
galaxies and PSF are measured with a weight function of identical size. We
demonstrate the accuracy and capabilities of this new method in the context of
weak gravitational lensing measurements with a set of specialized tests and
show its competitive performance on the GREAT08 challenge data. A complete C++
implementation of the method can be requested from the authors.
