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## Publications [#303547] of Mauro Maggioni

Papers Published

1. Iwen, MA; Maggioni, M, Approximation of Points on Low-Dimensional Manifolds Via Random Linear Projections, vol. 2 (February, 2013) [1204.3337v1], [doi]
(last updated on 2018/01/18)

Abstract:
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 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 manifold-based signal recovery is presented in the process of proving the two main results mentioned above.

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