  In this article we give an account of a method of smoothing spatial
inhomogeneous data sets by using wavelet reconstruction on a regular grid in an
auxilliary space onto which the original data is mapped. In a previous paper by
the present authors, we devised a method for inferring the velocity potential
from the radial component of the cosmic velocity field assuming an ideal
sampling. Unfortunately the sparseness of the real data as well as errors of
measurement require us to first smooth the velocity field as observed on a
3-dimensional support (i.e. the galaxy positions) inhomogeneously distributed
throughout the sampled volume. The wavelet formalism permits us to introduce a
minimal smoothing procedure that is characterized by the variation in size of
the smothing window function. Moreover the output smoothed radial velocity
field can be shown to correspond to a well defined theoretical quantity as long
as the spatial sampling support satisfies certain criteria. We argue also that
one should be very cautious when comparing the velocity potential derived from
such a smoothed radial component of the velocity field with related quantities
derived from other studies (e.g : of the density field).
