This paper establishes a high order condition on the restricted isometry property adapted to a frame D （D-RIF） for the signal recovery. It is shown that if the measurementmatrix A satisfies the D-RIP condition δtk ...This paper establishes a high order condition on the restricted isometry property adapted to a frame D （D-RIF） for the signal recovery. It is shown that if the measurementmatrix A satisfies the D-RIP condition δtk 〈t-1/t for t 〉 1, then all signals f which aresparse in terms of a tight frame D can be recovered stably or exactly via the l1-analysis model based on y= Af ＋ z in 12 and Dantzig selector bounded noise setting.展开更多
修正的多重正交最小二乘(modified multiple orthogonal least squares,m^(2)OLS)算法是在多重正交最小二乘算法(multiple orthogonal least squares,m OLS)的基础上提出的.利用m^(2)OLS算法能够从模型y=Ax+v中重构稀疏信号x.借助预选...修正的多重正交最小二乘(modified multiple orthogonal least squares,m^(2)OLS)算法是在多重正交最小二乘算法(multiple orthogonal least squares,m OLS)的基础上提出的.利用m^(2)OLS算法能够从模型y=Ax+v中重构稀疏信号x.借助预选取规则,m^(2)OLS算法的复杂度低于m OLS.在三类噪声干扰下,本文给出保证m^(2)OLS算法每次迭代至少选取一个正确指标的充分条件.该条件是在约束等距性质(restricted isometry property,RIP)框架下给出的.在第一次迭代中,本文给出m^(2)OLS算法不能选取正确指标的条件.与现有的结果相比,本文中的结果具有一定优势.展开更多
基金supported by National Natural Science Foundation of China(11271050 and 11371183)
文摘This paper establishes a high order condition on the restricted isometry property adapted to a frame D （D-RIF） for the signal recovery. It is shown that if the measurementmatrix A satisfies the D-RIP condition δtk 〈t-1/t for t 〉 1, then all signals f which aresparse in terms of a tight frame D can be recovered stably or exactly via the l1-analysis model based on y= Af ＋ z in 12 and Dantzig selector bounded noise setting.
基金supported by NSFC(Nos.11271050,11371183)Li was partially supported by NSFC(No.11171026)+1 种基金the Fundamental Research Funds for the Central Universities(No.2014kJJCA10)Beijing Higher Education Young Elite Teacher Project
基金The work was done when the first author visited Beijing Normal University and partly supported by National Natural Science Foundations(No.19970128,No.19901021)Natural Science Foundations of Beijing(No.1982005,No.1013006)a program for Returned Ove
