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H 1 Wavelets and signal processing: a match made in heaven

Auteurs : Vetterli, Martin (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : In this talk, we will briefly look at the history of wavelets, from signal processing algorithms originating in speech and image processing, and harmonic analysis constructions of orthonormal bases. We review the promises, the achievements, and some of the limitations of wavelet applications, with JPEG and JPEG2000 as examples. We then take two key insights from the wavelet and signal processing experience, namely the time-frequency-scale view of the world, and the sparsity property of wavelet expansions, and present two recent results. First, we show new bounds for the time-frequency spread of sequences, and construct maximally compact sequences. Interestingly they differ from sampled Gaussians. Next, we review work on sampling of finite rate of innovation signals, which are sparse continuous-time signals for which sampling theorems are possible. We conclude by arguing that the interface of signal processing and applied harmonic analysis has been both fruitful and fun, and try to identify lessons learned from this experience.

    Keywords: wavelets - filter banks - subband coding - uncertainty principle - sampling theory - sparse sampling

    Codes MSC :
    42C40 - Wavelets and other special systems
    65T60 - Wavelets (numerical methods)
    94A08 - Image processing (compression, reconstruction, etc.)
    94A12 - Signal theory (characterization, reconstruction, filtering, etc.)

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 25/03/15
      Date de captation : 23/01/15
      Collection : Special events ; 30 Years of Wavelets ; Computer Science ; Mathematics in Science and Technology
      Format : quicktime ; audio/x-aac
      Durée : 00:43:34
      Domaine : Mathematics in Science & Technology ; Computer Science
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-01-23_Vetterli.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 : 23/01/15 - 24/01/15
    Année de la rencontre : 2015
    URL Congrès : http://feichtingertorresani.weebly.com/3...

    Citation Data

    DOI : 10.24350/CIRM.V.18726803
    Cite this video as: Vetterli, Martin (2015). Wavelets and signal processing: a match made in heaven. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18726803
    URI : http://dx.doi.org/10.24350/CIRM.V.18726803


    1. [1] Barbotin, Y. Parametric estimation of sparse channels: theory and applications. Lausanne : EPFL, 2014, 187 p. - http://dx.doi.org/10.5075/epfl-thesis-5976

    2. [2] Blu, T., Dragotti, P.L., Vetterli, M., Marziliano, P., & Coulot, L. (2008). Sparse sampling of signal innovations. IEEE Signal Processing Magazine, 25(2), 31–40, 2008 - http://dx.doi.org/10.1109/msp.2007.914998

    3. [3] Parhizkar, R., Barbotin, Y., & Vetterli, M. (2014). Sequences with minimal time-frequency uncertainty. Applied and Computational Harmonic Analysis - http://dx.doi.org/10.1016/j.acha.2014.07.001

    4. [4] Parhizkar, R. Euclidean distance matrices: properties, algorithms and applications. Lausanne : EPFL, 2013, 125 p. - http://dx.doi.org/10.5075/epfl-thesis-5971

    5. [5] Vetterli, M., Kovacevic, J., & Goyal, V.K. (2014). Foundations of signal processing. Cambridge: Cambridge University Press - www.cambridge.org/9781107038608

    6. [6] Vetterli, M., Marziliano, P., & Blu, T. (2002). Sampling signals with finite rate of innovation. IEEE Transactions on Signal Processing, 50(6), 1417-1428 - http://dx.doi.org/10.1109/tsp.2002.1003065