Sparse Subspace Denoising for Image Manifolds

With the increasing availability of high dimensional data and demand in sophisticated data analysis algorithms, manifold learning becomes a critical technique to perform dimensionality reduction, unraveling the intrinsic data structure. The real-world data however often come with noises and outliers, seldom, all the data live in a single linear subspace. Inspired by the recent advances in sparse subspace learning and diffusion-based approaches, we propose a new manifold denoising algorithm in which data neighborhoods are adaptively inferred via sparse subspace reconstruction, we then derive a new formulation to perform denoising to the original data. Experiments carried out on both toy and real applications demonstrate the effectiveness of our method, it is insensitive to parameter tuning and we show significant improvement over the competing algorithms.