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# Multi angle

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Multi angle Compressive sensing with time-frequency structured random matrices

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

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 Format : quicktime ; audio/x-aac Durée : 00:35:41 Domaine : Analyse & Applications ; Numerical Analysis & Scientific Computing ; Probability & Statistics Audience : Chercheurs ; Doctorants , Post - Doctorants Download : http://videos.cirm-math.fr/2015-01-24_Rauhut.mp4 Informations sur la rencontre Nom du congrès : 30 years of wavelets / 30 ans des ondelettesOrganisteurs Congrès : Feichtinger, Hans G. ; Torrésani, BrunoDates : 23/01/2015 - 24/01/15 Année de la rencontre : 2015 URL Congrès : http://feichtingertorresani.weebly.com/3...Citation DataDOI : 10.24350/CIRM.V.18724603Cite this video as: Rauhut, Holger (2015). Compressive sensing with time-frequency structured random matrices.CIRM .Audiovisual resource. doi:10.24350/CIRM.V.18724603URI : http://dx.doi.org/10.24350/CIRM.V.18724603

Bibliographie

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

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