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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Volume 265, Pages 211–219 (Mi tm835)  
This article is cited in 2 scientific papers (total in 2 papers)

Optimization of Frame Representations for Compressed Sensing and Mercedes-Benz Frame

S. Ya. Novikov, I. S. Ryabtsov

Faculty of Mathematics and Mechanics, Samara State University, Samara, Russia
Full-text PDF (189 kB) Citations (2)
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Abstract: We prove that there is no single uniform tight frame in Euclidean (unitary) space such that a solution of the $\ell_1$-norm minimization problem for the frame representation is attained on the frame coefficients. Then we find an exact solution of the $\ell_1$-minimization problem for the Mercedes-Benz frame in $\mathbb R^N$. We also give some examples of connections between optimization problems of various types.
Received in October 2008
English version:
Proceedings of the Steklov Institute of Mathematics, 2009, Volume 265, Pages 199–207
DOI: https://doi.org/10.1134/S0081543809020187
Bibliographic databases:
UDC: 517.51+517.98
Language: English
Citation: S. Ya. Novikov, I. S. Ryabtsov, “Optimization of Frame Representations for Compressed Sensing and Mercedes-Benz Frame”, Selected topics of mathematical physics and $p$-adic analysis, Collected papers, Trudy Mat. Inst. Steklova, 265, MAIK Nauka/Interperiodica, Moscow, 2009, 211–219; Proc. Steklov Inst. Math., 265 (2009), 199–207
Citation in format AMSBIB
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\pages 211--219
\publ MAIK Nauka/Interperiodica
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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