L’échantillonnage compressé

Transcript

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.