In this paper the 3D minimum variance filtering problem is considered. The
proposed spatiotemporal filter is derived according to the assumption that
the 3D signal can be modelled by an ensemble of smooth 3D gaussian random f
ields. The resulting filtering algorithm is given by an optimal combination
of three 1D estimators and is endowed with an information on the location
about the spatiotemporal discontinuities of the signal. This allows the fil
ter to conciliate the two opposite requirements of an effective noise reduc
tion and edge preservation.