A Partial Derandomization of PhaseLift using Spherical Designs

Understand

The problem of retrieving phase information from amplitude measurements alone has appeared in many scientific disciplines over the last century.

• PhaseLift is a recently introduced algorithm for phase recovery that is computationally efficient, numerically stable, and comes with rigorous performance guarantees.
• PhaseLift is optimal in the sense that the number of amplitude measurements required for phase reconstruction scales linearly with the dimension of the signal.
• However, it specifically demands Gaussian random measurement vectors - a limitation that restricts practical utility and obscures the specific properties of measurement ensembles that enable phase retrieval.