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

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.