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Sbornik: Mathematics, 2017, Volume 208, Issue 11, Pages 1646–1660
DOI: https://doi.org/10.1070/SM8822 (Mi sm8822) 		 
Bounding the restricted isometry constants for a tight frame

I. E. Kaporin

Federal Research Center "Computer Science and Control" of Russian Academy of Sciences
English version PDF (475 kB)
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DOI: https://doi.org/10.1070/SM8822
Abstract: The standard restricted isometry condition for a tight frame (frequently used as a compressed sensing matrix) is considered, and deterministic lower bounds are obtained for the constants involved. These bounds depend only on the matrix sizes and sparsity level. The sharpness of the new estimates is discussed as well as their interplay with the existing compressed sensing theory.
Bibliography: 18 titles.
Keywords: compressed sensing, $k$-equivolume tight frame, restricted isometry property, Jacobi polynomials, extreme roots.
Funding agency Grant number
Russian Foundation for Basic Research 17-07-00510-а
Russian Academy of Sciences - Federal Agency for Scientific Organizations I.5П
Ministry of Education and Science of the Russian Federation НШ-8860.2016.1
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 17-07-00510-а), of the Presidium of the Russian Academy of Sciences (Programme for fundamental research I.5П “Problems of design of high-performance distributed and cloud systems and technologies. Intelligent information technologies and systems”), and also in the framework of the Programme of the President of the Russian Federation for the support of leading scientific schools (grant no. НШ-8860.2016.1).
Received: 23.09.2016 and 14.04.2017
Russian version:
Matematicheskii Sbornik, 2017, Volume 208, Number 11, Pages 75–89
DOI: https://doi.org/10.4213/sm8822
Bibliographic databases:
Document Type: Article
UDC: 512.643.8+517.538.3+519.142
MSC: Primary 42C15, 11C20; Secondary 65F15, 33C45
Language: English
Original paper language: Russian
Citation: I. E. Kaporin, “Bounding the restricted isometry constants for a tight frame”, Mat. Sb., 208:11 (2017), 75–89; Sb. Math., 208:11 (2017), 1646–1660
Citation in format AMSBIB
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    References:30
    First page:26
     
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