Phase Retrieval Meets Statistical Learning Theory: A Flexible Convex Relaxation

Understand

We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal.

• Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP) in methods such as PhaseLift and compete with recently developed non-convex techniques for phase retrieval.
• We relax the quadratic equations for phaseless measurements to inequality constraints each of which representing a symmetric "slab".
• Through a simple convex program, our proposed estimator finds an extreme point of the intersection of these slabs that is best aligned with a given anchor vector.