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

2013/04/06 by Balan, Radu
#Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1304.1839

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.

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