2015/04/12 by Erwin Riegler, Riegler, Erwin, Georg Tauböck +1
Computer Science · Mathematics · #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1504.03024
arxiv created 2015/04/22 · arxiv updated 2015/04/23
We propose an information-theoretic framework for phase retrieval. Specifically, we consider the problem of recovering an unknown n-dimensional vector x up to an overall sign factor from m=Rn phaseless measurements with compression rate R and derive a general achievability bound for R. Surprisingly, it turns out that this bound on the compression rate is the same as the one for almost lossless analog compression obtained by Wu and Verdú (2010): Phaseless linear measurements are as good as linear measurements with full phase information in the sense that ignoring the sign of m measurements only leaves us with an ambiguity with respect to an overall sign factor of x.