  Any method for estimating the ensemble average of arbitrary operator
(observables or not, including the density matrix) relates the quantity of
interest to a complete set of observables, i.e. a quorum}. This corresponds to
an expansion on an irreducible set of operators in the Liouville space. We give
two general characterizations of these sets. All the known unbiased
reconstruction techniques, i.e. ``quantum tomographies'', can be described in
this framework. New operatorial resolutions are given that can be used to
implement novel reconstruction schemes.
