  We study the symplectic Radon transform from the point of view of the
metaplectic representation of the symplectic group and its action on the
Lagrangian Grassmannian. We give rigorous proofs in the general setting of
multi-dimensional quantum systems. We interpret the inverse Radon transform as
a "demarginalization process" for the Wigner distribution. This work completes,
by giving complete proofs, a previous Note.
