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• W2051213905 abstract "For any 00, we give an efficient deterministic construction of a linear subspace V ⊆ Rn, of dimension (1-e)n in which the lp and lr norms are the same up to a multiplicative factor of poly(e-1) (after proper normalization). As a corollary we get a deterministic compressed sensing algorithm (Basis Pursuit) for a new range of parameters. In particular, for any constant e>0 and p Re n with the l1/lp guarantee for (n ⋅ poly(e))-sparse vectors. Namely, let x be a vector in Rn whose l1 distance from a k-sparse vector (for some k=n ⋅ poly(e)) is δ. The algorithm, given Ax as input, outputs an n dimensional vector y such that ||x-y||p ≤ δ k1/p-1. In particular this gives a weak form of the l2/l1 guarantee.Our construction has the additional benefit that when viewed as a matrix, A has at most O(1) non-zero entries in each row. As a result, both the encoding (computing Ax) and decoding (retrieving x from Ax) can be computed efficiently." @default.
• W2051213905 created "2016-06-24" @default.
• W2051213905 creator A5048818669 @default.
• W2051213905 date "2011-01-01" @default.
• W2051213905 modified "2023-09-25" @default.
• W2051213905 title "Deterministic construction of a high dimensional lpsection in l1nfor anyp<2" @default.
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• W2051213905 doi "https://doi.org/10.1145/1993636.1993722" @default.
• W2051213905 hasPublicationYear "2011" @default.
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