New Bounds for Restricted Isometry Constants
نویسندگان
چکیده
منابع مشابه
Improved Bounds on Restricted Isometry Constants
The restricted isometry constant (RIC) of a matrix A measures how close to an isometry is the action of A on vectors with few nonzero entries, measured in the 2 norm. Specifically, the upper and lower RICs of a matrix A of size n×N are the maximum and the minimum deviation from unity (one) of the largest and smallest, respectively, square of singular values of all (N k ) matrices formed by taki...
متن کاملImproved Bounds on Restricted Isometry Constants for Gaussian Matrices
The Restricted Isometry Constants (RIC) of a matrix A measures how close to an isometry is the action of A on vectors with few nonzero entries, measured in the `2 norm. Specifically, the upper and lower RIC of a matrix A of size n ×N is the maximum and the minimum deviation from unity (one) of the largest and smallest, respectively, square of singular values of all `N k ́ matrices formed by taki...
متن کاملBounds on restricted isometry constants of random matrices
In this paper we look at isometry properties of random matrices. During the last decade these properties gained a lot attention in a field called compressed sensing in first place due to their initial use in [7, 8]. Namely, in [7, 8] these quantities were used as a critical tool in providing a rigorous analysis of l1 optimization’s ability to solve an under-determined system of linear equations...
متن کاملNew Bounds for Restricted Isometry Constants in Low-rank Matrix Recovery
In this paper, we establish new bounds for restricted isometry constants (RIC) in low-rank matrix recovery. Let A be a linear transformation from Rm×n into Rp, and r the rank of recovered matrix X ∈ Rm×n. Our main result is that if the condition on RIC satisfies δ2r+k + 2( r k ) δmax{r+ 3 2 k,2k} < 1 for a given positive integer k ≤ m − r, then r-rank matrix can be exactly recovered via nuclear...
متن کاملA New Estimate of Restricted Isometry Constants for Sparse Solutions
We show that as long as the restricted isometry constant δ2k < 1/2, there exist a value q0 ∈ (0, 1] such that for any q < q0, each minimizer of the nonconvex `q minimization for the sparse solution of any underdetermined linear system is the sparse solution.
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2010
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2010.2054730