We present a new method for reconstructing two-dimensional mass maps o
f galaxy clusters from the image distortion of background galaxies. In
contrast to most previous approaches, which directly convert locally
averaged image ellipticities to mass maps (direct methods), our entrop
y-regularized maximum-likelihood method is an inverse approach. Albeit
somewhat more expensive computationally, our method allows high spati
al resolution in those parts of the cluster where the lensing signal i
s strong enough. Furthermore, it allows to straightforwardly incorpora
te additional constraints, such as magnification information or strong
-lensing features. Using synthetic data, we compare our new approach t
o direct methods and find indeed a substantial improvement especially
in the reconstruction of mass peaks. The main differences to previousl
y published inverse methods are discussed.