An Improved Estimate in the Restricted Isometry Problem
作者： Jean Bourgain
DOI: 10.1007/978-3-319-09477-9_5
关键词: Mathematics 、 Combinatorics 、 Orthogonal matrix 、 Logarithm 、 Bounded function 、 Restricted isometry property 、 Matrix (mathematics) 、 Binary logarithm 、 Unit (ring theory) 、 Isometry
摘要: It is shown that for the n × n-Hadamard matrix (or, more generally, a bounded orthogonal matrix) RIP-property r-space vectors holds, with row restriction to set S of size $$\displaystyle{\vert S\vert < C(\varepsilon )(\log n)^{2}(\log r)r.}$$ This bound represents slight improvement over (Rudelson and Vershynin, Commun Pure Appl Math 61:1025–1045, 2008) in power logarithm decreased by one unit.
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sci-hub.st 参考文章(1)
Mark Rudelson, Roman Vershynin, On sparse reconstruction from Fourier and Gaussian measurements Communications on Pure and Applied Mathematics. ,vol. 61, pp. 1025- 1045 ,(2008) , 10.1002/CPA.20227