  A frame $(x_j)_{j\in J}$ for a Hilbert space $H$ allows for a linear and
stable reconstruction of any vector $x\in H$ from the linear measurements
$(\langle x,x_j\rangle)_{j\in J}$. However, there are many situations where
some information in the frame coefficients is lost. In applications where one
is using sensors with a fixed dynamic range, any measurement above that range
is registered as the maximum, and any measurement below that range is
registered as the minimum. Depending on the context, recovering a vector from
such measurements is called either declipping or saturation recovery. We
initiate a frame theoretic approach to saturation recovery in a similar way to
what [BCE06] did for phase retrieval. We characterize when saturation recovery
is possible, show optimal frames for use with saturation recovery correspond to
minimal multi-fold packings in projective space, and prove that the classical
frame algorithm may be adapted to this non-linear problem to provide a
reconstruction algorithm.
