Error Lower Bound for Phase Retrieval

In phase retrieval problems, it is desired to estimate the phase of the Fourier transform of an object given measurements of the modulus (square root of intensity) of the Fourier transform. This is equivalent to estimating the object itself because of the Fourier transform relationship. Several iterative Fourier transform algorithms have had great success in making such object estimates from Fourier magnitude data and object constraint information [1,2]. However, other than through empirical results [3], it has not been known how the error in the object estimate depends on measurement noise, constraint information, and other parameters describing the problem.