The analysis of whole-sky galaxy surveys commonly suffers from the problems of shot-noise and incomplete sky coverage (e.g., at the Zone of Avoidance). The orthogonal set of spherical harmonics is utilized here to expand the observed galaxy distribution. We show that in the framework of Bayesian statistics and Gaussian random fields the 4π harmonics can be recovered and the shot-noise can be removed, 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 projected 1.2 Jy IRAS survey. The reconstruction confirms the connectivity of the supergalactic plane across the Galactic plane (at Galactic longitude l ∼ 135° and l ∼ 315°) and the Puppis cluster behind the Galactic plane (l ∼ 240°). The method can be extended to three dimensions in both real and redshift space, and applied to other cosmic phenomena such as the COBE microwave background maps.