2013/11/27 by Pohl, Volker, Yang, Fanny, Boche, Holger
#49N45 #90C22 #94A12 #94A20 #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1311.7045
The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a union of subspaces, respectively. A stable analytic reconstruction procedure of low complexity is given. Additionally it is proven that signal recovery from these measurements can be solved exactly via a semidefinite program. A practical implementation with 4 deterministic diffraction patterns is provided and some numerical experiments with noisy measurements complement the analytic approach.