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L’échantillonnage compressé

Avatar for Gabriel Peyré Gabriel Peyré
November 02, 2016

L’échantillonnage compressé

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

Avatar for Gabriel Peyré

Gabriel Peyré

November 02, 2016
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  1. Appareil photo à pixel unique •  Digital Micromirror Device (DMD)

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

    by Texas Instruments http://dsp.rice.edu/cscamera
  3. 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)
  4. 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)
  5. 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)
  6. 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)