This paper presents a novel scheme for image denoising. In spite of the sophistication of recent schemes, most algorithms show outstanding performance under their assumption, but totally fail in general cases and produce artifacts or destroy fine structures. Inspired by recent manifold learning methods, especially the locally linear embedding (LLE), our method utilizes the underlying fact that image patches in noisy and denoised images construct manifolds with similar local geometry in these two distinct spaces. According to LLE, we characterize local geometry by measuring how an image patch represented by a feature vector can be reconstructed by its nearest neighbors in feature space. Besides using the training image patches to construct the embedding, we also propose to overlap the target denoised image patches to satisfy local compatibility and smoothness constraints. The experimental results show that our method is flexible with noise type and achieves state-of-the-art performance particularly in terms of preserving the fine structures.