Locally Linear Denoising on Image Manifolds

Dian Gong, Fei Sha, Gérard Medioni
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:265-272, 2010.

Abstract

We study the problem of image denoising where images are assumed to be samples from low dimensional (sub)manifolds. We propose the algorithm of locally linear denoising. The algorithm approximates manifolds with locally linear patches by constructing nearest neighbor graphs. Each image is then locally denoised within its neighborhoods. A global optimal denoising result is then identified by aligning those local estimates. The algorithm has a closed-form solution that is efficient to compute. We evaluated and compared the algorithm to alternative methods on two image data sets. We demonstrated the effectiveness of the proposed algorithm, which yields visually appealing denoising results, incurs smaller reconstruction errors and results in lower error rates when the denoised data are used in supervised learning tasks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v9-gong10a, title = {Locally Linear Denoising on Image Manifolds}, author = {Gong, Dian and Sha, Fei and Medioni, Gérard}, booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics}, pages = {265--272}, year = {2010}, editor = {Teh, Yee Whye and Titterington, Mike}, volume = {9}, series = {Proceedings of Machine Learning Research}, address = {Chia Laguna Resort, Sardinia, Italy}, month = {13--15 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v9/gong10a/gong10a.pdf}, url = {https://proceedings.mlr.press/v9/gong10a.html}, abstract = {We study the problem of image denoising where images are assumed to be samples from low dimensional (sub)manifolds. We propose the algorithm of locally linear denoising. The algorithm approximates manifolds with locally linear patches by constructing nearest neighbor graphs. Each image is then locally denoised within its neighborhoods. A global optimal denoising result is then identified by aligning those local estimates. The algorithm has a closed-form solution that is efficient to compute. We evaluated and compared the algorithm to alternative methods on two image data sets. We demonstrated the effectiveness of the proposed algorithm, which yields visually appealing denoising results, incurs smaller reconstruction errors and results in lower error rates when the denoised data are used in supervised learning tasks.} }
Endnote
%0 Conference Paper %T Locally Linear Denoising on Image Manifolds %A Dian Gong %A Fei Sha %A Gérard Medioni %B Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2010 %E Yee Whye Teh %E Mike Titterington %F pmlr-v9-gong10a %I PMLR %P 265--272 %U https://proceedings.mlr.press/v9/gong10a.html %V 9 %X We study the problem of image denoising where images are assumed to be samples from low dimensional (sub)manifolds. We propose the algorithm of locally linear denoising. The algorithm approximates manifolds with locally linear patches by constructing nearest neighbor graphs. Each image is then locally denoised within its neighborhoods. A global optimal denoising result is then identified by aligning those local estimates. The algorithm has a closed-form solution that is efficient to compute. We evaluated and compared the algorithm to alternative methods on two image data sets. We demonstrated the effectiveness of the proposed algorithm, which yields visually appealing denoising results, incurs smaller reconstruction errors and results in lower error rates when the denoised data are used in supervised learning tasks.
RIS
TY - CPAPER TI - Locally Linear Denoising on Image Manifolds AU - Dian Gong AU - Fei Sha AU - Gérard Medioni BT - Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics DA - 2010/03/31 ED - Yee Whye Teh ED - Mike Titterington ID - pmlr-v9-gong10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 265 EP - 272 L1 - http://proceedings.mlr.press/v9/gong10a/gong10a.pdf UR - https://proceedings.mlr.press/v9/gong10a.html AB - We study the problem of image denoising where images are assumed to be samples from low dimensional (sub)manifolds. We propose the algorithm of locally linear denoising. The algorithm approximates manifolds with locally linear patches by constructing nearest neighbor graphs. Each image is then locally denoised within its neighborhoods. A global optimal denoising result is then identified by aligning those local estimates. The algorithm has a closed-form solution that is efficient to compute. We evaluated and compared the algorithm to alternative methods on two image data sets. We demonstrated the effectiveness of the proposed algorithm, which yields visually appealing denoising results, incurs smaller reconstruction errors and results in lower error rates when the denoised data are used in supervised learning tasks. ER -
APA
Gong, D., Sha, F. & Medioni, G.. (2010). Locally Linear Denoising on Image Manifolds. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:265-272 Available from https://proceedings.mlr.press/v9/gong10a.html.

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