Zhiqiang XU.The Minimal Measurement Number Problem in Phase Retrieval: A Review of Recent Developments[J].数学研究及应用,2017,37(1):40~46
The Minimal Measurement Number Problem in Phase Retrieval: A Review of Recent Developments
The Minimal Measurement Number Problem in Phase Retrieval: A Review of Recent Developments
投稿时间:2016-11-28  最后修改时间:2016-12-19
DOI:10.3770/j.issn:2095-2651.2017.01.004
中文关键词:  Phase retrieval  frames  measurement number  matrix recovery  bilinear form  algebraic geometry  embedding
英文关键词:Phase retrieval  frames  measurement number  matrix recovery  bilinear form  algebraic geometry  embedding
基金项目: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).
作者单位
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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中文摘要:
      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.
英文摘要:
      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.
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