This paper gives new bounds for restricted isometry constant(RIC)in compressed sensing.LetΦbe an m×n real matrix and k be a positive integer with k≤n.The main results of this paper show that if the restricted i...This paper gives new bounds for restricted isometry constant(RIC)in compressed sensing.LetΦbe an m×n real matrix and k be a positive integer with k≤n.The main results of this paper show that if the restricted isometry constant ofΦsat-isfiesδ8ak<1 andδk+ak<3/2−1+√(4a+3)^(2)−8/8aforα>3/8,then k-sparse solution can be recovered exactly via l1 minimization in the noiseless case.In particular,whenα=1,1.5,2 and3,we haveδ2k<0.5746 andδ8k<1,orδ2.5k<0.7046 andδ12k<1,orδ3k<0.7731 andδ16k<1 orδ4k<0.8445 andδ24k<1.展开更多
基金This work was partially supported by the National Basic Research Program of China(No.2010CB732501)the National Natural Science Foundation of China(No.11171018)+1 种基金d the Fundamental Research Funds for the Central Universities(No.2013JBM095)We thank the two anonymous referees for their very useful comments.
文摘This paper gives new bounds for restricted isometry constant(RIC)in compressed sensing.LetΦbe an m×n real matrix and k be a positive integer with k≤n.The main results of this paper show that if the restricted isometry constant ofΦsat-isfiesδ8ak<1 andδk+ak<3/2−1+√(4a+3)^(2)−8/8aforα>3/8,then k-sparse solution can be recovered exactly via l1 minimization in the noiseless case.In particular,whenα=1,1.5,2 and3,we haveδ2k<0.5746 andδ8k<1,orδ2.5k<0.7046 andδ12k<1,orδ3k<0.7731 andδ16k<1 orδ4k<0.8445 andδ24k<1.
