Phase Retrieval With Random Gaussian Sensing Vectors by Alternating Projections

@article{Waldspurger2018PhaseRW,
  title={Phase Retrieval With Random Gaussian Sensing Vectors by Alternating Projections},
  author={Irx00E8ne Waldspurger},
  journal={IEEE Transactions on Information Theory},
  year={2018},
  volume={64},
  pages={3301-3312}
}
We consider a phase retrieval problem, where we want to reconstruct a <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>-dimensional vector from its phaseless scalar products with <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> sensing vectors, independently sampled from complex normal distributions. We show that, with a suitable initialization procedure, the classical algorithm of alternating projections (Gerchberg–Saxton) succeeds with… CONTINUE READING
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