Linear embeddings of low-dimensional subsets of a Hilbert space to $\mathbb{R}^m$
Résumé
We consider the problem of embedding a low-dimensional set, M, from an infinite-dimensional Hilbert space, H, to a finite-dimensional space. Defining appropriate random linear projections, we propose two constructions of linear maps that have the restricted isometry property (RIP) on the secant set of M with high probability. The first one is optimal in the sense that it only needs a number of projections essentially proportional to the intrinsic dimension of M to satisfy the RIP. The second one, which is based on a variable density sampling technique, is computationally more efficient, while potentially requiring more measurements.
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Technical_report.pdf (306.23 Ko)
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EUSIPCO15-Embeddings_infinite_dimension.pdf (244.79 Ko)
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Origine | Fichiers produits par l'(les) auteur(s) |
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Origine | Fichiers produits par l'(les) auteur(s) |
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