  The maximum-entropy method is applied to the problem of reconstructing the
projected mass density of a galaxy cluster using its gravitational lensing
effects on background galaxies. We demonstrate the method by reconstructing the
mass distribution in a model cluster using simulated shear and magnification
data to which Gaussian noise is added. The mass distribution is reconstructed
directly and the inversion is regularised using the entropic prior for this
positive additive distribution. For realistic noise levels, we find that the
method faithfully reproduces the main features of the cluster mass distribution
not only within the observed field but also slightly beyond it. We estimate the
uncertainties on the reconstruction by calculating an analytic approximation to
the covariance matrix of the reconstruction values of each pixel. This result
is compared with error estimates derived from Monte-Carlo simulations for
different noise realisations and found to be in good agreement.
