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Learning multiscale sparse representations for image and video restoration

Publication ,  Journal Article
Mairal, J; Sapiro, G; Elad, M
Published in: Multiscale Modeling and Simulation
January 1, 2008

This paper presents a framework for learning multiscale sparse representations of color images and video with overcomplete dictionaries. A single-scale K-SVD algorithm was introduced in [M. Aharon, M. Elad, and A. M. Bruckstein, IEEE Trans. Signal Process., 54 (2006), pp. 4311-4322], formulating sparse dictionary learning for grayscale image representation as an optimization problem, efficiently solved via orthogonal matching pursuit (OMP) and singular value decomposition (SVD). Following this work, we propose a multiscale learned representation, obtained by using an efficient quadtree decomposition of the learned dictionary and overlapping image patches. The proposed framework provides an alternative to predefined dictionaries such as wavelets and is shown to lead to state-of-the-art results in a number of image and video enhancement and restoration applications. This paper describes the proposed framework and accompanies it by numerous examples demonstrating its strength. © 2008 Society for Industrial and applied Mathematics.

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Published In

Multiscale Modeling and Simulation

DOI

EISSN

1540-3467

ISSN

1540-3459

Publication Date

January 1, 2008

Volume

7

Issue

1

Start / End Page

214 / 241

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

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MLA
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Mairal, J., Sapiro, G., & Elad, M. (2008). Learning multiscale sparse representations for image and video restoration. Multiscale Modeling and Simulation, 7(1), 214–241. https://doi.org/10.1137/070697653
Mairal, J., G. Sapiro, and M. Elad. “Learning multiscale sparse representations for image and video restoration.” Multiscale Modeling and Simulation 7, no. 1 (January 1, 2008): 214–41. https://doi.org/10.1137/070697653.
Mairal J, Sapiro G, Elad M. Learning multiscale sparse representations for image and video restoration. Multiscale Modeling and Simulation. 2008 Jan 1;7(1):214–41.
Mairal, J., et al. “Learning multiscale sparse representations for image and video restoration.” Multiscale Modeling and Simulation, vol. 7, no. 1, Jan. 2008, pp. 214–41. Scopus, doi:10.1137/070697653.
Mairal J, Sapiro G, Elad M. Learning multiscale sparse representations for image and video restoration. Multiscale Modeling and Simulation. 2008 Jan 1;7(1):214–241.

Published In

Multiscale Modeling and Simulation

DOI

EISSN

1540-3467

ISSN

1540-3459

Publication Date

January 1, 2008

Volume

7

Issue

1

Start / End Page

214 / 241

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics