Math @ Duke

Publications [#303547] of Mauro Maggioni
Papers Published
 Iwen, MA; Maggioni, M, Approximation of Points on LowDimensional Manifolds Via Random Linear
Projections, vol. 2
(February, 2013) [1204.3337v1], [doi]
(last updated on 2018/07/20)
Abstract: This paper considers the approximate reconstruction of points, x \in R^D,
which are close to a given compact ddimensional 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 uniform approximation guarantees when the
number of linear measurements of x depends logarithmically on D. Finally, the
proofs of these facts are constructive: A practical algorithm for
manifoldbased signal recovery is presented in the process of proving the two
main results mentioned above.


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