Cited by 1,716Image and Signal Denoising MethodsSparse and Compressive Sensing TechniquesAdvanced Data Compression Techniques

Sparse Representation for Color Image Restoration

Open access
Mairal, Julien, Elad, Michael, Sapiro, Guillermo·2008·IEEE Transactions on Image Processing

Abstract

Sparse representations of signals have drawn considerable interest in recent years. The assumption that natural signals, such as images, admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data. In particular, the design of well adapted dictionaries for images has been a major challenge. The K-SVD has been recently proposed for this task and shown to perform very well for various grayscale image processing tasks. In this paper, we address the problem of learning dictionaries for color images and extend the K-SVD-based grayscale image denoising algorithm that appears in. This work puts forward ways for handling nonhomogeneous noise and missing information, paving the way to state-of-the-art results in applications such as color image denoising, demosaicing, and inpainting, as demonstrated in this paper.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1109/tip.2007.911828

Cites

60 of 60 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 8

  1. [4]4. S. Mallat, A Wavelet Tour of Signal Processing, Second Edition (Wavelet Analysis & Its Applications). Academic Press, September 1999.
  2. [6]6. --, "New tight frames of curvelets and the problem of approximating piecewise C 2 images with piecewise C 2 edges," Comm. Pure Appl. Math., vol. 57, pp. 219-266, February 2004.
  3. [8]8. M. Do and M. Vertterli, Contourlets, Beyond Wavelets, G. V. Welland, Ed. Academic Press, 2003.
  4. [13]13. E. P. Simoncelli, W. T. Freeman, E. H. Adelson, and D. J. Heeger, "Shiftable multi-scale transforms," IEEE Transactions on Informations Theory, vol. 38, no. 2, pp. 587-607, September 1992.
  5. [21]21. S. Mallat and Z. Zhang, "Matching pursuit in a time-frequency dictionary," IEEE Transactions on Signal Processing, vol. 41, no. 12, pp. 3397-3415, 1993.
  6. [28]28. E. Haber and L. Tenorio, "Learning regularization functionals," Inverse Problems, vol. 19, pp. 611-626, 2003.
  7. [36]36. M. F. Tappen, B. C. Russell, and W. T. Freeman, "Exploiting the sparse derivative prior for super-resolution and image demosaicing," in In IEEE Workshop on Statistical and Computational Theories of Vision, 2003.
  8. [52]52. X. Li, "Demosaicing by successive approximations," IEEE Transactions on Image Processing, vol. 14, no. 2, pp. 267-278, 2005.

Cited by

Sorted by citations

Authors
Mairal, J., Elad, M., & Sapiro, G.
Affiliations
  • University of Minnesota (US)
  • Technion – Israel Institute of Technology (IL)
Venue
IEEE Transactions on Image Processing
Published
2008-01
Volume
17
Issue
1
Pages
53-69
ISSN
1057-7149 (ISSN-L)
OpenAlex
W2114122776
Cited by
1,716
References
60
Citations by year
2026: 11 · 2025: 30 · 2024: 45 · 2023: 59 · 2022: 70 · 2021: 75 · 2020: 98 · 2019: 114 · 2018: 130 · 2017: 145 · 2016: 138 · 2015: 182 · 2014: 167 · 2013: 138 · 2012: 105
FWCI
45.96
Type
journal article
Language
en
Open access
Locations
  • IEEE Transactions on Image Processing (publishedVersion)
  • PubMed (publishedVersion)
  • University of Minnesota Digital Conservancy (University of Minnesota) (submittedVersion)
Funders
Defense Advanced Research Projects Agency
Topics
  • Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Signal Denoising Methods
  • Physical Sciences › Engineering › Computational Mechanics › Sparse and Compressive Sensing Techniques
  • Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Data Compression Techniques
Keywords
sparse representation, color image restoration, dictionary learning, K-SVD, color image denoising, demosaicing, image inpainting, missing information, redundant dictionaries
MeSH terms
Algorithms, Artificial Intelligence, Color, Colorimetry, Image Enhancement, Image Interpretation, Computer-Assisted, Pattern Recognition, Automated, Sensitivity and Specificity, Reproducibility of Results

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review