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

Abstract

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 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 the Cramer-Rao lower bound.

updated 6 Apr. 2013 version arXiv:1304.1839: to appear in Foundations of Computational Mathematics