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This paper is concerned with the question of reconstructing a vector in a finite-dimensional 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 as an iterative algorithm that finds the least-square solution, which is robust in the presence of noise. We analyze its numerical performance by comparing it to the Cramer---Rao lower bound.

Reconstruction of Signals from Magnitudes of Redundant Representations: The Complex Case