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H 1 Compressive sensing with time-frequency structured random matrices

Auteurs : Rauhut, Holger (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : 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

    Codes MSC :
    42C40 - Wavelets and other special systems
    60B20 - Random matrices (probabilistic aspects)
    90C25 - Convex programming
    94A08 - Image processing (compression, reconstruction, etc.)
    94A20 - Sampling theory

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 16/03/15
      Date de captation : 24/01/15
      Collection : Special events ; 30 Years of Wavelets ; Analysis and its Applications ; Probability and Statistics ; Numerical Analysis and Scientific Computing
      Format : quicktime ; audio/x-aac
      Durée : 00:35:41
      Domaine : Analysis and its Applications ; Numerical Analysis & Scientific Computing ; Probability & Statistics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-01-24_Rauhut.mp4

    Informations sur la rencontre

    Nom de la rencontre : 30 years of wavelets / 30 ans des ondelettes
    Organisateurs de la rencontre : Feichtinger, Hans G. ; Torrésani, Bruno
    Dates : 23/01/2015 - 24/01/15
    Année de la rencontre : 2015
    URL Congrès : http://feichtingertorresani.weebly.com/3...

    Citation Data

    DOI : 10.24350/CIRM.V.18724603
    Cite this video as: Rauhut, Holger (2015). Compressive sensing with time-frequency structured random matrices. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18724603
    URI : http://dx.doi.org/10.24350/CIRM.V.18724603


    1. [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. [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. [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. [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. [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