In this manuscript, we propose an efficient manifold denoiser based on landmark diffusion and optimal shrinkage under the complicated high dimensional noise and compact manifold setup. It is flexible to handle several setups, including the high ambient space dimension with a manifold embedding that occupies a subspace of high or low dimensions, and the noise could be colored and dependent. A systematic comparison with other existing algorithms on both simulated and real datasets is provided. This manuscript is mainly algorithmic and we report several existing tools and numerical results. Theoretical guarantees and more comparisons will be reported in the official paper of this manuscript.

翻译：本文提出一种基于地标扩散与最优收缩的高效流形去噪方法，适用于复杂高维噪声及紧致流形场景。该方法能灵活处理多种情形，包括：高维环境空间中嵌入低维或高维子空间的流形情形，以及噪声可具相关性及有色性。我们系统比较了该方法与其他现有算法在仿真数据集和真实数据集上的表现。本文侧重算法实现，展示了若干现有工具与数值结果。理论保障及更广泛的比较将在本文的正式版本中予以报告。