Projections and Phase retrieval

2015/06/01 by Edidin, Dan · 2 citations
#42C15 (secondary) 14P05 (secondary) #94A12 (primary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1506.00674

Abstract

We characterize collections of orthogonal projections for which it is possible to reconstruct a vector from the magnitudes of the corresponding projections. As a result we are able to show that in an M-dimensional real vector space a vector can be reconstructed from the magnitudes of its projections onto a generic collection of N ≥ 2M-1 subspaces. We also show that this bound is sharp when N = 2^k +1. The results of this paper answer a number of questions raised in \citeCCPW:13.

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