  We present a maximum probability approach to reconstructing spatial maps of
the peculiar velocity field at redshifts $z\sim0.1$, where the velocities have
been measured from distance indicators (DI) such as $D_n-\sigma$ relations or
Tully-Fisher. With the large statistical uncertainties associated with DIs, our
reconstruction method aims to recover the underlying true peculiar velocity
field by reducing these errors with the use of two physically motivated
filtering prior terms. The first constructs an estimate of the velocity field
derived from the galaxy over-density {\deltag} and the second makes use of the
matter linear density power spectrum {\pk}. Using $N$-body simulations we find,
with an SDSS-like sample ($N_{gal}\simeq33$ per deg$^2$), an average
correlation coefficient value of $r=0.55\pm{0.02}$ between our reconstructed
velocity field and that of the true velocity field from the simulation.
However, with a suitably high number density of galaxies from the next
generation surveys (e.g. $N_{gal}\simeq140$ per deg$^2$) we can achieve an
average $r=0.70\pm{0.02}$ out to moderate redshifts $z\sim0.1$. This will prove
useful for future tests of gravity, as these relatively deep maps are
complementary to weak lensing maps at the same redshift.
