The Minimal Measurement Number Problem in Phase Retrieval: A Review of Recent Developments
Received:November 28, 2016  Revised:December 19, 2016
Key Words: Phase retrieval   frames   measurement number   matrix recovery   bilinear form   algebraic geometry   embedding  
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11422113; 11331012; 91630203) and by National Basic Research Program of China (973 Program 2015CB856000).
Author NameAffiliation
Zhiqiang XU LSEC, Inst. Comp. Math., Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100091, P. R. China
University of Chinese Academy of Sciences, Beijing, 100049, P. R. China 
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Abstract:
      Phase retrieval is to recover the signals from phaseless measurements which is raised in many areas. A fundamental problem in phase retrieval is to determine the minimal measurement number $m$ so that one can recover $d$-dimensional signals from $m$ phaseless measurements. This problem attracts much attention of experts from different areas. In this paper, we review the recent development on the minimal measurement number and also raise many interesting open questions.
Citation:
DOI:10.3770/j.issn:2095-2651.2017.01.004
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