In the phase retrieval problem, a signal must be recovered from the magnitude of its Fourier transform. The signal's compressibility can be used as prior knowledge to aid in its recovery. This knowledge also allows for recovery from fewer Fourier modulus measurements than the signal's bandwidth alone would dictate. We introduce a compressibility constraint for phase retrieval, define the number of measurements necessary for phase retrieval of sparse signals, and apply these concepts to terahertz imaging.