A frame (x_j) for a Hilbert space H allows for a linear and stable reconstruction of any vector x in H from the linear measurements (<x,x_j>).  However, there are many situations where some information of the frame coefficients is lost.   In applications such as signal processing and electrical engineering one often uses sensors with a limited effective range and any measurement above that range is registered as the maximum.  Depending on the context, recovering a vector from such measurements is called either declipping or saturation recovery.  We will discuss a frame theoretic approach to this problem in a similar way to what Balan, Casazza, and Edidin did for phase retrieval.  The talk is based on joint work with W. Alharbi,  D. Ghoreishi, B. Johnson, and N. Randrianarivony.