English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

The phase retrieval problem has garnered significant attention since thedevelopment of the PhaseLift algorithm, which is a convex program that operatesin a lifted space of matrices. Because of the substantial computational costdue to lifting, many approaches to phase retrieval have been developed,including non-convex optimization algorithms which operate in the naturalparameter space, such as Wirtinger Flow. Very recently, a convex formulationcalled PhaseMax has been discovered, and it has been proven to achieve phaseretrieval via linear programming in the natural parameter space under optimalsample complexity. The current proofs of PhaseMax rely on statistical learningtheory or geometric probability theory. Here, we present a short and elementaryproof that PhaseMax exactly recovers real-valued vectors from randommeasurements under optimal sample complexity. Our proof only relies on standardprobabilistic concentration and covering arguments, yielding a simpler and moredirect proof than those that require statistical learning theory, geometricprobability or the highly technical arguments for Wirtinger Flow-likeapproaches.

An Elementary Proof of Convex Phase Retrieval in the Natural Parameter Space via the Linear Program PhaseMax