  We present a new Unbiased Minimal Variance (UMV) estimator for the purpose of
reconstructing the large--scale structure of the universe from noisy, sparse
and incomplete data. Similar to the Wiener Filter (WF), the UMV estimator is
derived by requiring the linear minimal variance solution given the data and an
assumed prior model specifying the underlying field covariance matrix. However,
unlike the WF, the minimization is carried out with the added constraint of an
unbiased reconstructed mean field. The new estimator does not necessitate a
noise model to estimate the underlying field; however, such a model is required
for evaluating the errors at each point in space. The general application of
the UMV estimator is to predict the values of the reconstructed field in
un-sampled regions of space (e.g., interpolation in the unobserved Zone of
Avoidance), and to dynamically transform from one measured field to another
(e.g., inversion of radial peculiar velocities to over-densities). Here, we
provide two very simple applications of the method. The first, is to recover a
1D signal from noisy, convolved data with gaps, e.g., CMB time-ordered data.
The second application is a reconstruction of the density and 3D peculiar
velocity fields from mock SEcat galaxy peculiar velocity catalogs.
