  Quantum Mechanical weak values are an interference effect measured by the
cross-Wigner transform W({\phi},{\psi}) of the post-and preselected states,
leading to a complex quasi-distribution {\rho}_{{\phi},{\psi}}(x,p) on phase
space. We show that the knowledge of {\rho}_{{\phi},{\psi}}(z) and of one of
the two functions {\phi},{\psi} unambiguously determines the other, thus
generalizing a recent reconstruction result of Lundeen and his collaborators.
