00:00:00 / 00:00:00

Compressive sensing with time-frequency structured random matrices

By Holger Rauhut

Appears in collections : Special events, 30 Years of Wavelets, 30 years of wavelets / 30 ans des ondelettes, 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

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.18724603
  • Cite this video 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

Bibliography

  • [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

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow




Register

  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
    community
  • Get notification updates
    for your favorite subjects
Give feedback