The peculiar velocities of galaxies can serve as excellent cosmological probes provided that the biases inherent to their measurements are contained prior to the start of any study. This paper proposes a new algorithm based on an object point process model whose probability density is built to statistically reduce the effects of Malmquist biases and uncertainties due to lognormal errors in radial peculiar velocity catalogs. More precisely, a simulated annealing algorithm allows for the probability density describing the point process model to be maximized. The resulting configurations are bias-minimized catalogs. We conducted tests on synthetic catalogs mimicking the second and third distance modulus catalogs of the Cosmicflows project from which peculiar velocity catalogs are derived. By reducing the local peculiar velocity variance in catalogs by an order of magnitude, the algorithm permits the recovery of the expected one, while preserving the small-scale velocity correlation. It also allows for the expected clustering to be retrieved. The algorithm was then applied to the observational catalogs. The large-scale structure reconstructed with the Wiener-filter technique applied to the bias-minimized observational catalogs matches that of the local cosmic web well, as supported by redshift surveys of local galaxies. These new bias-minimized versions of peculiar velocity catalogs can be used as a starting point for several studies, from plausible estimations of the most probable value for the Hubble constant, H 0 , to the production of simulations constrained to reproduce the local Universe.