  A new notion of dual fusion frame has been recently introduced by the
authors. In this article that notion is further motivated and it is shown that
it is suitable to deal with questions posed in a finite-dimensional real or
complex Hilbert space, reinforcing the idea that this concept of duality solves
the question about an appropriate definition of dual fusion frames. It is shown
that for overcomplete fusion frames there always exist duals different from the
canonical one. Conditions that assure the uniqueness of duals are given. The
relation of dual fusion frame systems with dual frames and dual projective
reconstruction systems is established. Optimal dual fusion frames for the
reconstruction in case of erasures of subspaces, and optimal dual fusion frame
systems for the reconstruction in case of erasures of local frame vectors are
determined. Examples that illustrate the obtained results are exhibited.
