Open AccessJournal Article
Extensions of Lipschitz mappings into Hilbert space
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This article is published in Contemporary mathematics.The article was published on 1984-01-01 and is currently open access. It has received 2789 citations till now. The article focuses on the topics: Lipschitz continuity & Hilbert space.read more
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Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
Emmanuel J. Candès,Terence Tao +1 more
TL;DR: If the objects of interest are sparse in a fixed basis or compressible, then it is possible to reconstruct f to within very high accuracy from a small number of random measurements by solving a simple linear program.
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Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
Emmanuel J. Candès,Terence Tao +1 more
TL;DR: In this article, it was shown that if the objects of interest are sparse or compressible in the sense that the reordered entries of a signal $f \in {\cal F}$ decay like a power-law, then it is possible to reconstruct $f$ to within very high accuracy from a small number of random measurements.
Proceedings ArticleDOI
Approximate nearest neighbors: towards removing the curse of dimensionality
Piotr Indyk,Rajeev Motwani +1 more
TL;DR: In this paper, the authors present two algorithms for the approximate nearest neighbor problem in high-dimensional spaces, for data sets of size n living in R d, which require space that is only polynomial in n and d.
Journal ArticleDOI
Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions
TL;DR: This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for performing low-rank matrix approximation, and presents a modular framework for constructing randomized algorithms that compute partial matrix decompositions.
Journal ArticleDOI
A Simple Proof of the Restricted Isometry Property for Random Matrices
TL;DR: In this article, the authors give a simple technique for verifying the restricted isometry property for random matrices that underlies compressive sensing, and obtain simple and direct proofs of Kashin's theorems on widths of finite balls in Euclidean space.
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Approximate nearest neighbors: towards removing the curse of dimensionality
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