  Quantum state reconstruction on a finite number of copies of a quantum system
with informationally incomplete measurements does, as a rule, not yield a
unique result. We derive a reconstruction scheme where both the likelihood and
the von Neumann entropy functionals are maximized in order to systematically
select the most-likely estimator with the largest entropy, that is the
least-bias estimator, consistent with a given set of measurement data. This is
equivalent to the joint consideration of our partial knowledge and ignorance
about the ensemble to reconstruct its identity. An interesting structure of
such estimators will also be explored.
