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

The Reconstruction Problem and Weak Quantum Values