Phase retrieval with random Gaussian sensing vectors by alternating projections

Irène Waldspurger (1, 2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales

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.

Domaines: Statistiques [math.ST]

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⟩