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# Locally Linear Denoising on Image Manifolds

*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.