Section: New Results

Phase retrieval with random Gaussian sensing vectors by alternating projections

I. Waldspurger

[16]

We consider the phase retrieval problem that consists in reconstructing a vector from its phaseless scalar products with sensing vectors independently sampled from complex normal distributions. In the previous two years, several new non-convex algorithms have been introduced to solve it, and have been proven to succeed with high probability. In this work, we show that the same success guarantees hold true for the oldest and most well-known phase retrieval algorithm, namely alternating projections (Gerchberg-Saxton), provided that it is carefully initialized. We conjecture that this result is still true when no special initialization procedure is used, and present numerical experiments that support this conjecture.