In the existing work,the recovery of strictly k-sparse signals with partial support information was derived in theℓ2 bounded noise setting.In this paper,the recovery of approximately k-sparse signals with partial supp...In the existing work,the recovery of strictly k-sparse signals with partial support information was derived in theℓ2 bounded noise setting.In this paper,the recovery of approximately k-sparse signals with partial support information in two noise settings is investigated via weightedℓp(0<p≤1)minimization method.The restricted isometry constant(RIC)conditionδt k<1 pη2 p−1+1 on the measurement matrix for some t∈[1+2−p 2+pσ,2]is proved to be sufficient to guarantee the stable and robust recovery of signals under sparsity defect in noisy cases.Herein,σ∈[0,1]is a parameter related to the prior support information of the original signal,andη≥0 is determined by p,t andσ.The new results not only improve the recent work in[17],but also include the optimal results by weightedℓ1 minimization or by standardℓp minimization as special cases.展开更多
Inspired by an interesting idea of Cai and Zhang,we formulate and prove the convex k-sparse decomposition of vectors that is invariant with respect to the l_(1) norm.This result fits well in discussing compressed sens...Inspired by an interesting idea of Cai and Zhang,we formulate and prove the convex k-sparse decomposition of vectors that is invariant with respect to the l_(1) norm.This result fits well in discussing compressed sensing problems under the Restricted Isometry property,but we believe it also has independent interest.As an application,a simple derivation of the RIP recovery conditionδk+θk,k<1 is presented.展开更多
基金supported in part by the National Natural Science Foundation of China under grant numbers 12171496 and U1811461in part by Guangdong Basic and Applied Basic Research Foundation under grant number 2020A1515010454in part by the Science and Technology Program of Guangzhou under grant number 201904010374.
文摘In the existing work,the recovery of strictly k-sparse signals with partial support information was derived in theℓ2 bounded noise setting.In this paper,the recovery of approximately k-sparse signals with partial support information in two noise settings is investigated via weightedℓp(0<p≤1)minimization method.The restricted isometry constant(RIC)conditionδt k<1 pη2 p−1+1 on the measurement matrix for some t∈[1+2−p 2+pσ,2]is proved to be sufficient to guarantee the stable and robust recovery of signals under sparsity defect in noisy cases.Herein,σ∈[0,1]is a parameter related to the prior support information of the original signal,andη≥0 is determined by p,t andσ.The new results not only improve the recent work in[17],but also include the optimal results by weightedℓ1 minimization or by standardℓp minimization as special cases.
基金This research was partially supported by the National 973 Project of China(No.2013CB834205)Zhiqiang Xu was supported by National Natural Science foundation of China(Nos.11171336,11331012,11021101)National Basic Research Program of China(973 Program No.2010CB832702).
文摘Inspired by an interesting idea of Cai and Zhang,we formulate and prove the convex k-sparse decomposition of vectors that is invariant with respect to the l_(1) norm.This result fits well in discussing compressed sensing problems under the Restricted Isometry property,but we believe it also has independent interest.As an application,a simple derivation of the RIP recovery conditionδk+θk,k<1 is presented.
