  In this paper, we study the Hilbert$-$Schmidt frame (HS-frame) theory for
separable Hilbert spaces. We first present some characterizations of HS-frames
and prove that HS-frames share many important properties with frames. Then, we
show how the inverse of the HS-frame operator can be approximated using
finite-dimensional methods. Finally, we present a classical perturbation result
and prove that HS-frames are stable under small perturbations.
