Shira Faigenbaum-Golovin

Paper abstract:
In this paper, we present a method for denoising and reconstructing a low-dimensional manifold in a high-dimensional space. We introduce a multidimensional extension of the Locally Optimal Projection algorithm which was proposed by Lipman et al. in 2007 for surface reconstruction in 3D. The high-dimensional generalization bypasses the curse of dimensionality while reconstructing the manifold in high dimension. The effectiveness of our approach is demonstrated in various numerical experiments, by considering different manifold topologies with various amounts of noise, including a case of a manifold of different co-dimensions at different locations.