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Matematicheskie Zametki, 2007, Volume 82, Issue 6, Pages 829–837
DOI: https://doi.org/10.4213/mzm4183
(Mi mzm4183)
 

This article is cited in 78 scientific papers (total in 78 papers)

A Remark on Compressed Sensing

B. S. Kashina, V. N. Temlyakovb

a Steklov Mathematical Institute, Russian Academy of Sciences
b University of South Carolina
References:
Abstract: Recently, a new direction in signal processing – “Compressed Sensing” is being actively developed. A number of authors have pointed out a connection between the Compressed Sensing problem and the problem of estimating the Kolmogorov widths, studied in the seventies and eighties of the last century. In this paper we make the above mentioned connection more precise.
Keywords: compressed sensing, signal processing, Kolmogorov width, Gelfand width, sparsity, restricted isometry property, combinatorial optimization problem.
Received: 15.08.2007
English version:
Mathematical Notes, 2007, Volume 82, Issue 6, Pages 748–755
DOI: https://doi.org/10.1134/S0001434607110193
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: B. S. Kashin, V. N. Temlyakov, “A Remark on Compressed Sensing”, Mat. Zametki, 82:6 (2007), 829–837; Math. Notes, 82:6 (2007), 748–755
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  • This publication is cited in the following 78 articles:
    1. A. P. Solodov, V. N. Temlyakov, “Vosstanovlenie po znacheniyam v tochkakh v funktsionalnykh klassakh so strukturnym usloviem”, Matem. zametki, 117:4 (2025), 543–560  mathnet  crossref
    2. Fengong Wu, Penghong Zhong, Huasong Xiao, Chunmei Miao, “Frame-based block sparse compressed sensing via $l_2/l_1$-synthesis”, EURASIP J. Adv. Signal Process., 2024:1 (2024)  crossref
    3. Yongping Liu, Man Lu, “Approximation problems on the smoothness classes”, Acta Math Sci, 44:5 (2024), 1721  crossref
    4. Venkatesan Guruswami, Jun-Ting Hsieh, Prasad Raghavendra, 2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS), 2024, 930  crossref
    5. A. M. Iosevich, B. S. Kashin, I. V. Limonova, A. Mayeli, “Subsystems of orthogonal systems and the recovery of sparse signals in the presence of random losses”, Russian Math. Surveys, 79:6 (2024), 1095–1097  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    6. Ke-Lin Du, M. N. S. Swamy, Zhang-Quan Wang, Wai Ho Mow, “Matrix Factorization Techniques in Machine Learning, Signal Processing, and Statistics”, Mathematics, 11:12 (2023), 2674  crossref
    7. K. Z. Najiya, Munnu Sonkar, C. S. Sastry, “Local Recovery Bounds for Prior Support Constrained Compressed Sensing”, Math. Notes, 111:1 (2022), 93–102  mathnet  mathnet  crossref  isi  scopus
    8. E. E. Egorova, G. A. Kabatiansky, “Separable collusion-secure multimedia codes”, Problems Inform. Transmission, 57:2 (2021), 178–198  mathnet  crossref  crossref  isi
    9. Sasmal P., Theeda P., Jampana Ph.V., Sastry Ch.S., “Nullspace Property For Optimality of Minimum Frame Angle Under Invertible Linear Operators”, IEEE Signal Process. Lett., 28 (2021), 1928–1932  crossref  isi
    10. d'Orsi T., Novikov G., Steurer D., “Consistent Regression When Oblivious Outliers Overwhelm”, Proceedings of Machine Learning Research, 139, eds. Meila M., Zhang T., Jmlr-Journal Machine Learning Research, 2021  isi
    11. Sasmal P., Jampana Ph., Sastry Ch.S., “Construction of Binary Matrices as a Union of Orthogonal Blocks Via Generalized Euler Squares”, IEEE Signal Process. Lett., 28 (2021), 882–886  crossref  isi
    12. Jameson Cahill, Dustin G. Mixon, Applied and Numerical Harmonic Analysis, Excursions in Harmonic Analysis, Volume 6, 2021, 343  crossref
    13. Roulet V., Boumal N., d'Aspremont A., “Computational Complexity Versus Statistical Performance on Sparse Recovery Problems”, Inf. Inference, 9:1 (2020), 1–32  crossref  mathscinet  isi  scopus
    14. Licheng Jiao, Ronghua Shang, Fang Liu, Weitong Zhang, Brain and Nature-Inspired Learning Computation and Recognition, 2020, 109  crossref
    15. Li G., Yan J., Gu Yu., “Information Theoretic Lower Bound of Restricted Isometry Property Constant”, 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (Icassp), International Conference on Acoustics Speech and Signal Processing Icassp, IEEE, 2019, 5297–5301  isi
    16. Gen Li, Jingkai Yan, Yuantao Gu, ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019, 5297  crossref
    17. Bandeira A.S., Lewis M.E., Mixon D.G., “Discrete Uncertainty Principles and Sparse Signal Processing”, J. Fourier Anal. Appl., 24:4 (2018), 935–956  crossref  mathscinet  isi  scopus
    18. Algorithmic Aspects of Machine Learning, 2018, 150  crossref
    19. Algorithmic Aspects of Machine Learning, 2018, 48  crossref
    20. Algorithmic Aspects of Machine Learning, 2018, 132  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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