  We propose a novel technique to refine the modelling of galaxy clusters mass
distribution using gravitational lensing. The idea is to combine the strengths
of both "parametric" and "non-parametric" methods to improve the quality of the
fit. We develop a multi-scale model that allows sharper contrast in regions of
higher density where the number of constraints is generally higher. Our model
consists of (i) a multi-scale grid of radial basis functions with physically
motivated profiles and (ii) a list of galaxy-scale potentials at the location
of the cluster member galaxies. This arrangement of potentials of different
sizes allows to reach a high resolution for the model with a minimum number of
parameters. We apply our model to the well studied cluster Abell 1689. We
estimate the quality of our mass reconstruction with a Bayesian MCMC sampler.
For a selected subset of multiple images, we manage to halve the errors between
the predicted and observed image positions compared to previous studies. This
owes to the flexibility of multi-scale models at intermediate scale between
cluster and galaxy scale. The software developed for this paper is part of the
public lenstool package which can be found at www.oamp.fr/cosmology/lenstool.
