In this paper we give an account of a method of smoothing spatial inho
mogeneous data sets by using wavelet reconstruction on a regular grid
in an auxilliary space onto which the original data is mapped. In a pr
evious paper by the present authors, we devised a method for inferring
the velocity potential from the radial component of the cosmic veloci
ty field assuming an ideal sampling. Unfortunately the sparseness of t
he real data (the peculiar velocities of galaxies) as well as errors o
f measurement require us to first smooth the velocity field as observe
d on a three-dimensional support (i.e. the galaxy positions) inhomogen
eously distributed throughout the sampled volume. The wavelet formalis
m permits us to introduce a minimal smoothing procedure that is charac
terized by the variation in size of the smoothing window function. Mor
eover, the output-smoothed radial velocity field can be shown to corre
spond to a well defined theoretical quantity as long as the spatial sa
mpling support satisfies certain criteria. We also argue that one shou
ld be very cautious when comparing the velocity potential derived from
such a smoothed radial component of the velocity field with related q
uantities derived from other studies (e.g. of the density field).