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.
Publications
Dian Gong, Fei Sha and Gerard Medioni, "Locally Linear Denoising on Image Manifolds", Proc. of the 13th International Conference on Artifical Intelligence and Statistics (AISTATS 2010), Sardinia, Italy, May 2010. Volume 9 of Journal of Machine Learning Research: W&CP 9. [Poster] [Project Webpage]
Selected References
Matthias Hein and Markus Maier, "Manifold Denoising", Advances in Neural Information Processing Systems (NIPS 2007), Vancouver, B.C., Canada, December 2006.
Matthias Hein and Markus Maier, "Manifold Denoising as Preprocessing for Finding Natural Representations of Data", Proceedings of the Twenty-Second AAAI Conference on Artificial Intelligence (AAAI 2007), Vancouver, B.C. Canada, July 2007.
Yee Whye Teh and Sam Roweis, "Automatic Alignment of Local Representations. ", Advances in Neural Information Processing Systems (NIPS 2003), Vancouver, B.C., Canada, December 2002.
Philippos Mordohai and Gerard Medioni, "Dimensionality Estimation, Manifold Learning and Function Approximation using Tensor Voting", Journal of Machine Learning Research (JMLR), 11, pp. 1-40, January 2010.
Acknowledgements
This work is supported in part by NIH Grant EY016093 (Dian Gong and Gerard Medioni) and NSF Grant 0957742 (Fei Sha).