Learning sparse representationsLearning sparse representationsto restore, classify, and sense images and videos

Guillermo Sapirop

University of Minnesota

Supported by NGA, ONR, DARPA, ARO, NSF, NIH

Compressive LecturingCompressive Lecturing

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Ramirez

Martin Duarte

Lecumberry

Rodriguez

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For the past ~2 years …• Introduce and Extend the K-SVD

– Denoising– Demosaicing– Inpainting– Mairal, Elad, Sapiro, IEEE-TIP, January 2008

• Learn multiscale dictionaries– Mairal, Elad, Sapiro, SIAM-MMS, April 2008

• Incoherent dictionaries– Ramirez, Lecumberry, Sapiro, January 2009, pre-print

• Learning to classify– Mairal, Bach, Ponce, Sapiro, Zisserman, CVPR 2008, NIPS 2008Mairal, Bach, Ponce, Sapiro, Zisserman, CVPR 2008, NIPS 2008– Rodriguez and Sapiro, pre-print, 2008.

• Learning to sense sparse signals– Duarte and Sapiro pre-print May 2008 IEEE-TIP to appear

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Duarte and Sapiro, pre print, May 2008, IEEE TIP to appear

The Sparseland Model for Images

M Every column in D (dictionary) is M Ka prototype signal (Atom).

NN The vector α

contains very few (say L) non-zeros.

=x

N

DA fixed Dictionary A sparse

& random vector

xD α

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What Should the Dictionary D Be?

α=≤α−α=α ˆx̂L.t.sy21

minargˆ 00

22

DDα 2

D should be chosen such that it sparsifies the representations (for a given task!)

Learn D :

Multiscale LearningOne approach to choose D is from a known set of transforms (Steerable

Color Image Examples

Task / sensing adapted

Internal structure

wavelet, Curvelet, Contourlets, Bandlets, …)

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Internal structure

Dictionaries for Reconstruction

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Color multiscale dictionaries

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Example: Non-uniform noise

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Example: Inpainting

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Learning multiple reconstructive and discriminative dictionaries

With J. Mairal, F. Bach, J. Ponce, and A. Zisserman, CVPR ’08, NIPS ‘08

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, , , , ,

Semi-supervised detection learningp g

MIT -- Learning Sparsity 12

Supervised Dictionary Learning

With J. Mairal, F. Bach, J. Ponce, and A. Zisserman, NIPS ‘08

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, , , ,

Learning Incoherent Dictionaries

• Optimization depends on the incoherence• Improved generalization properties• Improved classificationImproved classification

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Results

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Results

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Learning for Compressed Sensing

+ “RIP (Identity Gramm Matrix)”

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Design the dictionary and sensing togethertogether

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Just Believe the PicturesJust Believe the Pictures

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Just Believe the PicturesJust Believe the Pictures

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Just Believe the PicturesJust Believe the Pictures

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Conclusions• State-of-the-art denoising results for still

(shared with Dabov et al ) and video(shared with Dabov et al.) and video• Vectorial and multiscale learned

dictionariesdictionaries• Dictionary learning with internal structure• Dictionary learning for classification• Dictionary learning for classification• Dictionary learning for sensing

• Dictionary learning for the task• Optimization is dictionary dependent

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p y p

Please do not use the wrong dictionaries thanksdictionaries… thanks

• 12 M pixel image• 7 million patches7 million patches• LARS+online

learning:learning: ~8 minutes

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