L’échantillonnage compressé

E34ded36efe4b7abb12510d4e525fee8?s=47 Gabriel Peyré
November 02, 2016

L’échantillonnage compressé

Conférence "Hommage à Claude Shannon, le père de la théorie de l'information" au CIRM

E34ded36efe4b7abb12510d4e525fee8?s=128

Gabriel Peyré

November 02, 2016
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  1. Gabriel Peyré www.numerical-tours.com L’échantillonnage compressé É C O L E

    N O R M A L E S U P É R I E U R E
  2. Echantillonner puis compresser 0,1,0,. . . Lena Lena.bmp Lena.jpg

  3. Echantillonner puis compresser 0,1,0,. . . Lena Lena.bmp Lena.jpg

  4. Echantillonner puis compresser 0,1,0,. . . Lena Lena.bmp Lena.jpg

  5. Appareil photo à pixel unique •  Digital Micromirror Device (DMD)

    by Texas Instruments http://dsp.rice.edu/cscamera
  6. Appareil photo à pixel unique •  Digital Micromirror Device (DMD)

    by Texas Instruments http://dsp.rice.edu/cscamera
  7. Modèle mathématique de l’acquisition

  8. Modèle mathématique de l’acquisition

  9. Modèle mathématique de l’acquisition

  10. Modèle mathématique de l’acquisition

  11. Système linéaire

  12. Système linéaire

  13. Système linéaire

  14. Compressibilité et reconstruction Implication of sparsity: image “compression” 1 Compute

    1,000,000 wavelet coe cients of mega-pixel image 2 Set to zero all but the 25,000 largest coe cients 3 Invert the wavelet transform original image after zeroing out smallest coe cients This principle underlies modern lossy coders (sound, still-picture, video) Implication of sparsity: image “compression” 1 Compute 1,000,000 wavelet coe cients of mega-pixel image 2 Set to zero all but the 25,000 largest coe cients 3 Invert the wavelet transform original image after zeroing out smallest coe cients This principle underlies modern lossy coders (sound, still-picture, video)
  15. Compressibilité et reconstruction Implication of sparsity: image “compression” 1 Compute

    1,000,000 wavelet coe cients of mega-pixel image 2 Set to zero all but the 25,000 largest coe cients 3 Invert the wavelet transform original image after zeroing out smallest coe cients This principle underlies modern lossy coders (sound, still-picture, video) Implication of sparsity: image “compression” 1 Compute 1,000,000 wavelet coe cients of mega-pixel image 2 Set to zero all but the 25,000 largest coe cients 3 Invert the wavelet transform original image after zeroing out smallest coe cients This principle underlies modern lossy coders (sound, still-picture, video)
  16. La théorie de Candès et al. mplication of sparsity: image

    “compression” 1 Compute 1,000,000 wavelet coe cients of mega-pixel image 2 Set to zero all but the 25,000 largest coe cients 3 Invert the wavelet transform original image after zeroing out smallest coe cients his principle underlies modern lossy coders (sound, still-picture, video) Implication of sparsity: image “compression” 1 Compute 1,000,000 wavelet coe cients of mega-pixel image 2 Set to zero all but the 25,000 largest coe cients 3 Invert the wavelet transform original image after zeroing out smallest coe cients This principle underlies modern lossy coders (sound, still-picture, video) Implication of sparsity: image “compression” 1 Compute 1,000,000 wavelet coe cients of mega-pixel image 2 Set to zero all but the 25,000 largest coe cients 3 Invert the wavelet transform original image after zeroing out smallest coe cients This principle underlies modern lossy coders (sound, still-picture, video) Implication of sparsity: image “compression” 1 Compute 1,000,000 wavelet coe cients of mega-pixel image 2 Set to zero all but the 25,000 largest coe cients 3 Invert the wavelet transform original image after zeroing out smallest coe cients This principle underlies modern lossy coders (sound, still-picture, video)
  17. La théorie de Candès et al. mplication of sparsity: image

    “compression” 1 Compute 1,000,000 wavelet coe cients of mega-pixel image 2 Set to zero all but the 25,000 largest coe cients 3 Invert the wavelet transform original image after zeroing out smallest coe cients his principle underlies modern lossy coders (sound, still-picture, video) Implication of sparsity: image “compression” 1 Compute 1,000,000 wavelet coe cients of mega-pixel image 2 Set to zero all but the 25,000 largest coe cients 3 Invert the wavelet transform original image after zeroing out smallest coe cients This principle underlies modern lossy coders (sound, still-picture, video) Implication of sparsity: image “compression” 1 Compute 1,000,000 wavelet coe cients of mega-pixel image 2 Set to zero all but the 25,000 largest coe cients 3 Invert the wavelet transform original image after zeroing out smallest coe cients This principle underlies modern lossy coders (sound, still-picture, video) Implication of sparsity: image “compression” 1 Compute 1,000,000 wavelet coe cients of mega-pixel image 2 Set to zero all but the 25,000 largest coe cients 3 Invert the wavelet transform original image after zeroing out smallest coe cients This principle underlies modern lossy coders (sound, still-picture, video)
  18. Problèmes Inverses

  19. Problèmes Inverses

  20. Conclusion Claude Shannon, p` ere fondateur de la th´ eorie

    de l’information.
  21. Conclusion Claude Shannon, p` ere fondateur de la th´ eorie

    de l’information.
  22. Conclusion Claude Shannon, p` ere fondateur de la th´ eorie

    de l’information.