Approximation of Points on Low-Dimensional Manifolds Via Random Linear Projections

@article{Iwen2012ApproximationOP,
  title={Approximation of Points on Low-Dimensional Manifolds Via Random Linear Projections},
  author={Mark A. Iwen and Mauro Maggioni},
  journal={ArXiv},
  year={2012},
  volume={abs/1204.3337}
}
This paper considers the approximate reconstruction of points, x \in R^D, which are close to a given compact d-dimensional submanifold, M, of R^D using a small number of linear measurements of x. In particular, it is shown that a number of measurements of x which is independent of the extrinsic dimension D suffices for highly accurate reconstruction of a given x with high probability. Furthermore, it is also proven that all vectors, x, which are sufficiently close to M can be reconstructed with… 
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