  A statistical method for reconstructing large scale structure behind the Zone
of Avoidance is presented. It also corrects for shot-noise and for redshift
distortion in galaxy surveys. The galaxy distribution is expanded in an
orthogonal set of spherical harmonics. We show that in the framework of
Bayesian statistics and Gaussian random fields the $4 \pi$ harmonics can be
recovered and the shot-noise can be suppressed, giving the optimal picture of
the underlying density field. The correction factor from observed to
reconstructed harmonics turns out to be the well-known Wiener filter (the ratio
of signal to signal+noise), which is also derived by requiring minimum
variance. We apply the method to the 1.2 Jy IRAS survey. A reconstruction of
the projected galaxy distribution confirms the connectivity of the
Supergalactic Plane across the Galactic Plane (at Galactic longitude $l \sim
135^o$ and $l \sim 315^o$) and the Puppis cluster behind the Galactic Plane ($
l \sim 240^o$). The method is extended to 3-D, and is used to recover from the
1.2 Jy redshift survey the density, velocity and potential fields in the local
universe.
