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.
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