Weak Lensing Galaxy Cluster Field Reconstruction
  In this paper, we compare three methods to reconstruct galaxy cluster density
fields with weak lensing data. The first method called FLens integrates an
inpainting concept to invert the shear field with possible gaps, and a
multi-scale entropy denoising procedure to remove the noise contained in the
final reconstruction, that arises mostly from the random intrinsic shape of the
galaxies. The second and third methods are based on a model of the density
field made of a multi-scale grid of radial basis functions. In one case, the
model parameters are computed with a linear inversion involving a singular
value decomposition. In the other case, the model parameters are estimated
using a Bayesian MCMC optimization implemented in the lensing software
Lenstool. Methods are compared on simulated data with varying galaxy density
fields. We pay particular attention to the errors estimated with resampling. We
find the multi-scale grid model optimized with MCMC to provide the best
results, but at high computational cost, especially when considering
resampling. The SVD method is much faster but yields noisy maps, although this
can be mitigated with resampling. The FLens method is a good compromise with
fast computation, high signal to noise reconstruction, but lower resolution
maps. All three methods are applied to the MACS J0717+3745 galaxy cluster
field, and reveal the filamentary structure discovered in Jauzac et al. 2012.
We conclude that sensitive priors can help to get high signal to noise, and
unbiased reconstructions.
