  An optimal estimator of quantum states based on a modified Kalman Filter is
presented in this work. Such estimator acts after state measurement, allowing
to obtain an optimal estimation of quantum state resulting in the output of any
quantum image algorithm. Besides, a new criteria, logic, and arithmetic based
on projections onto vertical axis of Bloch Sphere exclusively are presented
too. This approach will allow us: 1) a simpler development of logic and
arithmetic quantum operations, where they will closer to those used in the
classical digital image processing algorithms, 2) building simple and robust
classical-to-quantum and quantum-to-classical interfaces. Said so far is
extended to quantum algorithms outside image processing too. In a special
section on metrics and simulations, three new metrics based on the comparison
between the classical and quantum versions algorithms for filtering and edge
detection of images are presented. Notable differences between the results of
classical and quantum versions of such algorithms (outside and inside of
quantum computer, respectively) show the need for modeling state and
measurement noise inside estimation scheme.
