  Galaxy peculiar velocities are excellent cosmological probes provided that
biases inherent to their measurements are contained before 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 permits maximizing
the probability density describing the point process model. The resulting
configurations are bias-minimized catalogs. Tests are conducted 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 recovering the expected one while preserving
the small-scale velocity correlation. It also permits retrieving the expected
clustering. The algorithm is then applied to the observational catalogs. The
large-scale structure reconstructed with the Wiener-filter technique applied to
the bias-minimized observational catalogs matches with great success the local
cosmic web as depicted 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 possibly estimating the most probable Hubble
constant, H0, value to the production of simulations constrained to reproduce
the local Universe.
