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Reconstruction of Signals from Magnitudes of Redundant Representations (1207.1134v1)
Published 4 Jul 2012 in math.FA, cs.IT, math.IT, and stat.AP
Abstract: 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.