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
A greedy algorithm used for the recovery of sparse signals,multiple orthogonal least squares(MOLS)have recently attracted quite a big of attention.In this paper,we consider the number of iterations required for the MO...A greedy algorithm used for the recovery of sparse signals,multiple orthogonal least squares(MOLS)have recently attracted quite a big of attention.In this paper,we consider the number of iterations required for the MOLS algorithm for recovery of a K-sparse signal x∈R^(n).We show that MOLS provides stable reconstruction of all K-sparse signals x from y=Ax+w in|6K/ M|iterations when the matrix A satisfies the restricted isometry property(RIP)with isometry constantδ_(7K)≤0.094.Compared with the existing results,our sufficient condition is not related to the sparsity level K.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 the National Natural Science Foundation of China(61907014,11871248,11701410,61901160)Youth Science Foundation of Henan Normal University(2019QK03).
文摘A greedy algorithm used for the recovery of sparse signals,multiple orthogonal least squares(MOLS)have recently attracted quite a big of attention.In this paper,we consider the number of iterations required for the MOLS algorithm for recovery of a K-sparse signal x∈R^(n).We show that MOLS provides stable reconstruction of all K-sparse signals x from y=Ax+w in|6K/ M|iterations when the matrix A satisfies the restricted isometry property(RIP)with isometry constantδ_(7K)≤0.094.Compared with the existing results,our sufficient condition is not related to the sparsity level K.
