  Time-symmetric quantum mechanics can be described in the usual
Weyl--Wigner--Moyal formalism (WWM) by using the properties of the Wigner
distribution, and its generalization, the cross-Wigner distribution. The use of
the latter makes clear a strongly oscillating interference between the pre- and
post-selected states. This approach allows us to give explicit formulas for the
state reconstruction problem, thus generalizing known results to the case of
arbitrary observables. In a forthcoming paper we will extend these results to
other quantization schemes.
