  High quality reconstructions of the three dimensional velocity and density
fields of the local Universe are essential to study the local Large Scale
Structure. In this paper, the Wiener Filter reconstruction technique is applied
to galaxy radial peculiar velocity catalogs to understand how the Hubble
constant (H0) value and the grouping scheme affect the reconstructions. While
H0 is used to derive radial peculiar velocities from galaxy distance
measurements and total velocities, the grouping scheme serves the purpose of
removing non linear motions. Two different grouping schemes (based on the
literature and a systematic algorithm) as well as five H0 values ranging from
72 to 76 km/s/Mpc are selected. The Wiener Filter is applied to the resulting
catalogs. Whatever grouping scheme is used, the larger H0 is, the larger the
infall onto the local Volume is. However, this conclusion has to be strongly
mitigated: a bias minimization scheme applied to the catalogs after grouping
suppresses this effect. At fixed H0, reconstructions obtained with catalogs
grouped with the different schemes exhibit structures at the proper location in
both cases but the latter are more contrasted in the less aggressive scheme
case: having more constraints permits an infall from both sides onto the
structures to reinforce their overdensity. Such findings highlight the
importance of a balance between grouping to suppress non linear motions and
preserving constraints to produce an infall onto structures expected to be
large overdensities. Such an observation is promising to perform constrained
simulations of the local Universe including its massive clusters.
