  We apply a mass reconstruction technique to simulated large-scale structure
gravitational distortion maps, from 2.5' to 10 degree scales, for different
cosmological scenarii. The projected mass is reconstructed using a
non-parametric least square method after noise due to the galaxy intrinsic
ellipticities has been added on. The shearing of the galaxies is performed
using the full lensing equation, without any hypothesis like the weak lensing
approximation, or other linearization. It is shown that, in the reconstructed
maps the noise acts as a perfect uncorrelated Poisson noise, with no
propagation at large scales. The measured power spectrum and first four moments
of the convergence can be corrected accurately for this source of noise. Using
60 realizations for each model, we show that a weak lensing survey of 5x5
degrees with a typical sheared background population of 30 gal/arcmin^2 at a
redshift z_s=1, is able to probe the amplitude of the power spectrum with a few
percents accuracy. Such a survey would lead to a 6 sigma separation between
open (Omega=0.3) and flat (Omega=1) model. This separation is shown to be
robust against different hypothesis for the normalization or the shape of the
power spectrum, and does not require very deep surveys. The observational
strategy for an optimal measurement of the power spectrum and the moments of
the convergence is discussed.
