Reconstruction of Signals from Magnitudes of Redundant Representations

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.