Phase retrieval with random Gaussian sensing vectors by alternating projections

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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [30 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01645081
Contributor : Irène Waldspurger <>
Submitted on : Wednesday, November 22, 2017 - 7:08:34 PM
Last modification on : Thursday, April 26, 2018 - 10:28:50 AM

File

gerchberg_saxton_final.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01645081, version 1

Collections

Citation

Irène Waldspurger. Phase retrieval with random Gaussian sensing vectors by alternating projections. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, In press. ⟨hal-01645081⟩

Share

Metrics

Record views

143

Files downloads

135