Phase Retrieval via Wirtinger Flow: Theory and Algorithms

@article{Cands2015PhaseRV,
  title={Phase Retrieval via Wirtinger Flow: Theory and Algorithms},
  author={Emmanuel J. Cand{\`e}s and Xiaodong Li and Mahdi Soltanolkotabi},
  journal={IEEE Transactions on Information Theory},
  year={2015},
  volume={61},
  pages={1985-2007}
}
We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal x ∈ ℂn about which we have phaseless samples of the form yr = |〈ar, x〉|2, r = 1, ..., m (knowledge of the phase of these samples would yield a linear system). This paper develops a nonconvex formulation of the phase retrieval problem as well as a concrete solution algorithm. In a nutshell, this algorithm starts with a careful initialization obtained by means of… CONTINUE READING
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