  We consider the notion of finite dimensional reconstructions systems (RS's),
which includes the fusion frames as projective RS's. We study erasures, some
geometrical properties of these spaces, the spectral picture of the set of all
dual systems of a fixed RS, the spectral picture of the set of RS operators for
the projective systems with fixed weights and the structure of the minimizers
of the joint potential in this setting. We give several examples.
