  The peculiar velocity reconstruction methods allow one to have a deeper
insight into the distribution of dark matter: both to measure mean matter
density and to obtain the primordial density fluctuations. We present here the
Monge-Ampere-Kantorovitch method applied to mock catalogues mimicking in both
redshift and distance catalogues. After having discussed the results obtained
for a class of biases that may be corrected for, we focus on the systematics
coming from the unknown distribution of unobserved mass and from the
statistical relationship between mass and luminosity. We then show how to use
these systematics to put constraints on the dark matter distribution. Finally a
preliminary application to an extended version (c z < 3000 km/s) of the
Neighbour Galaxy Catalogue is presented. We recover the peculiar velocities in
our neighbourhood and present a preliminary measurement of the local Omega_M.
