  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.
