  Weak lensing measurements are starting to provide statistical maps of the
distribution of matter in the universe that are increasingly precise and
complementary to cosmic microwave background maps. The probability distribution
(PDF) provides a powerful tool to test non-Gausian features in the convergence
field and to discriminate the different cosmological models. In this letter, we
present a new PDF space Wiener filter approach to reconstruct the probability
density function of the convergence from the noisy convergence field. We find
that for parameters comparable to the CFHT legacy survey, the averaged PDF of
the convergence in a 3 degree field can be reconstructed with an uncertainty of
about 10%, even though the pointwise PDF is noise dominated.
