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Journal Articles IEEE Transactions on Information Theory Year : 2018

Phase retrieval with random Gaussian sensing vectors by alternating projections

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Abstract

We consider a phase retrieval problem, where we want to reconstruct a n-dimensional vector from its phaseless scalar products with m 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 high probability when m ≥ Cn, for some C > 0. We conjecture that this result is still true when no special initialization procedure is used, and present numerical experiments that support this conjecture.
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Dates and versions

hal-01645081 , version 1 (22-11-2017)

Identifiers

  • HAL Id : hal-01645081 , version 1

Cite

Irène Waldspurger. Phase retrieval with random Gaussian sensing vectors by alternating projections. IEEE Transactions on Information Theory, 2018, 64 (5), pp.3301-3312. ⟨hal-01645081⟩
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