Galaxy distances and derived radial peculiar velocity catalogs constitute valuable datasets to study the dynamics of the Local Universe. However, such catalogs suffer from biases whose effects increase with the distance. Malmquist biases and lognormal error distribution affect the catalogs. Velocity fields of the Local Universe reconstructed with these catalogs present a spurious overall infall onto the Local Volume if they are not corrected for biases. Such an infall is observed in the reconstructed velocity field obtained when applying the BayesianWiener-Filter technique to the raw second radial peculiar velocity catalog of the Cosmicflows project. In this paper, an iterative method to reduce spurious non-Gaussianities in the radial peculiar velocity distribution, to retroactively derive overall better distance estimates resulting in a minimization of the effects of biases, is presented. This method is tested with mock catalogs. To control the cosmic variance, mocks are built out of different cosmological constrained simulations which resemble the Local Universe. To realistically reproduce the effects of biases, the mocks are constructed to be look-alikes of the second data release of the Cosmicflows project, with respect to the size, distribution of data and distribution of errors. Using a suite of mock catalogs, the outcome of the correction is verified to be affected neither by the added error realization, nor by the datapoint selection, nor by the constrained simulation. Results are similar for the different tested mocks. After correction, the general infall is satisfactorily suppressed. The method allows us to obtained catalogs which together with the Wiener-Filter technique give reconstructions approximating non biased velocity fields at 100-150 km/s (2-3 Mpc/h in terms of linear displacement), the linear theory threshold.

Accepted for publication in MNRAS, 13 pages, 10 figures, 1 table