Phase retrieval and norm retrieval

2014/09/29 by Saeid Bahmanpour, Bahmanpour, Saeid, Jameson Cahill +7
Engineering · Mathematics · Physics and Astronomy · #Advanced X-ray Imaging Techniques #FOS: Mathematics #Functional Analysis (math.FA) #Non-Destructive Testing Techniques #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1409.8266

openalex publication_date 2014/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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. One fundamental result: a frame \φ_i\_i=1^M yields phase retrieval if and only if \Tφ_i\_i=1^M yields norm retrieval for every invertible operator T.

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