Manifold Learning for Image Denoising

This paper presents a novel scheme for image denoising. In spite of the sophistication of recently developed double-density discrete wavelet transforms (double-density DWTs), it still produces artifacts or destroys fine structures by blurring the data. Inspired by recent manifold learning methods, especially the locally linear embedding (LLE), we discover the underlying fact that image patches in noisy and denoised images construct manifolds with similar local geometry in these two distinct spaces. Therefore, 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. In our method, double-density DWTs is incorporated with LLE for the purpose of denoising. 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