Manifold reconstruction and denoising from scattered data in high dimension
نویسندگان
چکیده
In this paper, we present a method for denoising and reconstruction of low-dimensional manifold in high-dimensional space. We suggest multidimensional extension the Locally Optimal Projection algorithm which was introduced by Lipman et al. 2007 surface 3D. The bypasses curse dimensionality avoids need carrying out dimensional reduction. It is based on non-convex optimization problem, leverages generalization outlier robust L1-median to higher dimensions while generating noise-free quasi-uniformly distributed points reconstructing unknown manifold. develop new prove that it converges local stationary solution with bounded linear rate convergence case starting point close enough minimum. addition, show its approximation order $O(h^2)$, where $h$ representative distance between given points. demonstrate effectiveness our approach considering different topologies various amounts noise, including co-dimensions at locations.
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2023
ISSN: ['0377-0427', '1879-1778', '0771-050X']
DOI: https://doi.org/10.1016/j.cam.2022.114818