Phase retrieval and norm retrieval

Understand

Phase retrieval has become a very active area of research.

• We will classify when phase retrieval by Parseval frames passes to the Naimark complement and when phase retrieval by projections passes to the orthogonal complements.
• We introduce a new concept we call norm retrieval and show that this is what is necessary for passing phase retrieval to complements.
• This leads to a detailed study of norm retrieval and its relationship to phase retrieval.