Phase retrieval and norm retrieval

被引：20

作者：

Bahmanpour, Saeid ^{[1
]}

Cahill, Jameson ^{[2
]}

Casazza, Peter G. ^{[1
]}

Jasper, John ^{[3
]}

Woodland, Lindsey M. ^{[1
]}

机构：

[1] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[2] Duke Univ, Dept Math, Durham, NC 27708 USA

[3] Univ Oregon, Dept Math, Eugene, OR 97403 USA

来源：

TRENDS IN HARMONIC ANALYSIS AND ITS APPLICATIONS | 2015年 / 650卷

关键词：

Phase retrieval; norm retrieval; frames; RECONSTRUCTION;

D O I：

10.1090/conm/650/13047

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 {phi(i)}(i=1)(M) wan yields phase retrieval if and only if {T phi(i)}(i=1)(M) yields norm retrieval for every invertible operator T.

引用

页码：3 / 14

页数：12

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