Two rounds of local averaging move a noisy high-dimensional sample to within O(σ√d) of a d-dimensional manifold, proven for the first time at noise levels comparable to the manifold's reach.
A non-local algorithm for image de- noising
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Local Averaging Accurately Distills Manifold Structure From Noisy Data
Two rounds of local averaging move a noisy high-dimensional sample to within O(σ√d) of a d-dimensional manifold, proven for the first time at noise levels comparable to the manifold's reach.