30 years of wavelets / 30 ans des ondelettes

Collection 30 years of wavelets / 30 ans des ondelettes

Organisateur(s) Feichtinger, Hans G. ; Torrésani, Bruno
Date(s) 23/01/2015 - 24/01/2015
URL associée https://www.chairejeanmorlet.com/1523.html
00:00:00 / 00:00:00
13 18

Compressive sensing with time-frequency structured random matrices

De Holger Rauhut

Apparaît également dans les collections : Special events, 30 Years of Wavelets, Actions thématiques

One of the important "products" of wavelet theory consists in the insight that it is often beneficial to consider sparsity in signal processing applications. In fact, wavelet compression relies on the fact that wavelet expansions of real-world signals and images are usually sparse. Compressive sensing builds on sparsity and tells us that sparse signals (expansions) can be recovered from incomplete linear measurements (samples) efficiently. This finding triggered an enormous research activity in recent years both in signal processing applications as well as their mathematical foundations. The present talk discusses connections of compressive sensing and time-frequency analysis (the sister of wavelet theory). In particular, we give on overview on recent results on compressive sensing with time-frequency structured random matrices.

Keywords: compressive sensing - time-frequency analysis - wavelets - sparsity - random matrices - $\ell_1$-minimization - radar - wireless communications

Informations sur la vidéo

Données de citation

  • DOI 10.24350/CIRM.V.18724603
  • Citer cette vidéo Rauhut, Holger (24/01/2015). Compressive sensing with time-frequency structured random matrices. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18724603
  • URL https://dx.doi.org/10.24350/CIRM.V.18724603

Bibliographie

  • [1] Foucart, S., & Rauhut, H. (2013). A mathematical introduction to compressive sensing. New York, NY: Birkhäuser/Springer. (Applied and Numerical Harmonic Analysis) - http://dx.doi.org/10.1007/978-0-8176-4948-7
  • [2] Krahmer, F., Mendelson, S., & Rauhut, H. (2014). Suprema of chaos processes and the restricted isometry property. Communications on Pure and Applied Mathematics, 67(11), 1877-1904 - http://dx.doi.org/10.1002/cpa.21504
  • [3] Krahmer, F., & Rauhut, H. (2014). Structured random measurements in signal processing. GAMM-Mitteilungen, 37(2),217-238 - http://dx.doi.org/10.1002/gamm.201410010
  • [4] Pfander, G., Rauhut, H., & Tropp, J. (2013). The restricted isometry property for time-frequency structured random matrices. Probability Theory and Related Fields, 156(3-4), 707-737 - http://dx.doi.org/10.1007/s00440-012-0441-4
  • [5] Pfander, G., Rauhut, H. (2010). Sparsity in time-frequency representations. The Journal of Fourier Analysis and Applications, 16(2), 233-260 - http://dx.doi.org/10.1007/s00041-009-9086-9

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