  We establish dilation theorems for non-tight frames with additional
structure, i.e., frames generated by unitary groups of operators and projective
unitary representations. This generalizes previous dilation results for
Parseval frames due to Han and Larson and Gabardo and Han. We also extend the
dilation theorem for Parseval wavelets, due to Dutkay, Han, Picioroaga, and Sun
, by identifying the optimal class of frame wavelets for which dilation into an
orthonormal wavelet is possible.
