  This paper is concerned with the question of reconstructing a vector in a
finite-dimensional real or complex Hilbert space when only the magnitudes of
the coefficients of the vector under a redundant linear map are known. We
present new invertibility results as well an iterative algorithm that finds the
least-square solution and is robust in the presence of noise. We analyze its
numerical performance by comparing it to two versions of the Cramer-Rao lower
bound.
