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Discovering local geometry of low-dimensional manifold embedded into a high-dimensional space has been widely studied in the literature of machine learning. Counter-intuitively, we will show for the class of signal-independent additive noise, noisy data do not destroy the manifold structure thanks to the blessing of dimensionality. Based on this observation, we propose to reconstruct the manifold for a collection of exemplars by alternating between image filtering and neighborhood search. The byproduct of such manifold reconstruction from noisy data is an exemplar-Based EM-like (EBEM) denoising algorithm with minimal number of control parameters. Despite its conceptual simplicity, EBEM can achieve comparable performance to other leading algorithms in the literature. Our results suggest the importance of understanding the physical origin of manifold constraint underlying natural images - the symmetry in natural scenes.