Quantum Homodyne Tomography as an Informationally Complete Positive   Operator Valued Measure
  We define a positive operator valued measure $E$ on $[0,2\pi]\times R$ describing the measurement of randomly sampled quadratures in quantum homodyne tomography, and we study its probabilistic properties. Moreover, we give a mathematical analysis of the relation between the description of a state in terms of $E$ and the description provided by its Wigner transform. 
P. Albini, E. De Vito, A. Toigo