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New bounds for restricted isometry constants
 LINGCHEN KONG, LEVENT TUNÇEL, NAIHUA XIU
, 2010
"... Abstract—This paper discusses new bounds for restricted isometry constants in compressed sensing. Let 8 be an n2p real matrix and k be a positive integer with k n. One of the main results of this paper shows that if the restricted isometry constant k of 8 satisfies k < 0:307 then ksparse signals ..."
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Cited by 54 (7 self)
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Abstract—This paper discusses new bounds for restricted isometry constants in compressed sensing. Let 8 be an n2p real matrix and k be a positive integer with k n. One of the main results of this paper shows that if the restricted isometry constant k of 8 satisfies k < 0:307 then k
On Support Sizes of Restricted Isometry Constants
, 2009
"... A generic tool for analyzing sparse approximation algorithms is the restricted isometry property (RIP) introduced by Candès and Tao. For qualitative comparison of sufficient conditions derived from an RIP analysis, the support size of the RIP constants is generally reduced as much as possible with t ..."
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Cited by 5 (2 self)
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A generic tool for analyzing sparse approximation algorithms is the restricted isometry property (RIP) introduced by Candès and Tao. For qualitative comparison of sufficient conditions derived from an RIP analysis, the support size of the RIP constants is generally reduced as much as possible
Challenging Restricted Isometry Constants with Greedy Pursuit
"... Abstract—This paper proposes greedy numerical schemes to compute lower bounds of the restricted isometry constants that are central in compressed sensing theory. Matrices with small restricted isometry constants enable stable recovery from a small set of random linear measurements. We challenge this ..."
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Cited by 1 (0 self)
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Abstract—This paper proposes greedy numerical schemes to compute lower bounds of the restricted isometry constants that are central in compressed sensing theory. Matrices with small restricted isometry constants enable stable recovery from a small set of random linear measurements. We challenge
IMPROVED BOUNDS ON RESTRICTED ISOMETRY CONSTANTS FOR GAUSSIAN MATRICES
"... Abstract. 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 ℓ2 norm. Specifically, the upper and lower RIC of a matrix A of size n × N is the maximum and the minimum deviation from unity (on ..."
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Cited by 31 (4 self)
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Abstract. 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 ℓ2 norm. Specifically, the upper and lower RIC of a matrix A of size n × N is the maximum and the minimum deviation from unity
1 Decay Properties of Restricted Isometry Constants
"... Abstract—Many sparse approximation algorithms accurately recover the sparsest solution to an underdetermined system of equations provided the matrix’s restricted isometry constants (RICs) satisfy certain bounds. There are no known large deterministic matrices that satisfy the desired RIC bounds; how ..."
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Cited by 7 (3 self)
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Abstract—Many sparse approximation algorithms accurately recover the sparsest solution to an underdetermined system of equations provided the matrix’s restricted isometry constants (RICs) satisfy certain bounds. There are no known large deterministic matrices that satisfy the desired RIC bounds
A New Estimate of Restricted Isometry Constants for Sparse Solutions
, 2011
"... 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 ℓq minimization for the sparse solution of any underdetermined linear system is the sparse solution. 1 ..."
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Cited by 5 (0 self)
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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 ℓq minimization for the sparse solution of any underdetermined linear system is the sparse solution. 1
Sparse recovery algorithms: Sufficient conditions in terms of restricted isometry constants
 Proceedings of the 13th International Conference on Approximation Theory
"... Abstract We review three recovery algorithms used in Compressive Sensing for the reconstruction ssparse vectors x ∈ CN from the mere knowledge of linear measurements y = Ax ∈ Cm, m < N. For each of the algorithms, we derive improved conditions on the restricted isometry constants of the measurem ..."
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Cited by 43 (3 self)
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Abstract We review three recovery algorithms used in Compressive Sensing for the reconstruction ssparse vectors x ∈ CN from the mere knowledge of linear measurements y = Ax ∈ Cm, m < N. For each of the algorithms, we derive improved conditions on the restricted isometry constants
Some Bounds and the Conditional Maximum Bound for Restricted Isometry Constants
"... Received:28/07/2013 Accepted:28/10/2014 Compressed sensing seeks to recover an unknown sparse signal with p entries by making far fewer than p measurements. The restricted isometry Constants (RIC) has become a dominant tool used for such cases since if RIC satisfies some bound then sparse signals ar ..."
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Received:28/07/2013 Accepted:28/10/2014 Compressed sensing seeks to recover an unknown sparse signal with p entries by making far fewer than p measurements. The restricted isometry Constants (RIC) has become a dominant tool used for such cases since if RIC satisfies some bound then sparse signals
Results 1  10
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386