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
The use of frames is analyzed in Compressed Sensing (CS) through proofs and experiments. First, a new generalized Dictionary-Restricted Isometry Property (D-RIP) sparsity bound constant for CS is established. Second, ...The use of frames is analyzed in Compressed Sensing (CS) through proofs and experiments. First, a new generalized Dictionary-Restricted Isometry Property (D-RIP) sparsity bound constant for CS is established. Second, experiments with a tight frame to analyze sparsity and reconstruction quality using several signal and image types are shown. The constant is used in fulfilling the definition of D-RIP. It is proved that k-sparse signals can be reconstructed if by using a concise and transparent argument1. The approach could be extended to obtain other D-RIP bounds (i.e. ). Experiments contrast results of a Gabor tight frame with Total Variation minimization. In cases of practical interest, the use of a Gabor dictionary performs well when achieving a highly sparse representation and poorly when this sparsity is not achieved.展开更多
This paper establishes new bounds on the restricted isometry constants with coherent tight frames in compressed sensing. It is shown that if the sensing matrix A satisfies the D-RIP condition 5k 〈 1/3 or 52k 〈 x/2/2...This paper establishes new bounds on the restricted isometry constants with coherent tight frames in compressed sensing. It is shown that if the sensing matrix A satisfies the D-RIP condition 5k 〈 1/3 or 52k 〈 x/2/2, then all signals f with D＊f are k-sparse can be recovered exactly via the constrained l1 minimization based on y = A f, where D＊ is the conjugate transpose of a tight frame D. These bounds are sharp when D is an identity matrix, see Cai and Zhang＇s work. These bounds are greatly improved comparing to the condition 8k 〈 0.307 or 52k 〈 0.4931. Besides, if 3k 〈 1/3 or δ2k 〈 √2/2, the signals can also be stably reconstructed in the noisy cases.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.
文摘The use of frames is analyzed in Compressed Sensing (CS) through proofs and experiments. First, a new generalized Dictionary-Restricted Isometry Property (D-RIP) sparsity bound constant for CS is established. Second, experiments with a tight frame to analyze sparsity and reconstruction quality using several signal and image types are shown. The constant is used in fulfilling the definition of D-RIP. It is proved that k-sparse signals can be reconstructed if by using a concise and transparent argument1. The approach could be extended to obtain other D-RIP bounds (i.e. ). Experiments contrast results of a Gabor tight frame with Total Variation minimization. In cases of practical interest, the use of a Gabor dictionary performs well when achieving a highly sparse representation and poorly when this sparsity is not achieved.
文摘This paper establishes new bounds on the restricted isometry constants with coherent tight frames in compressed sensing. It is shown that if the sensing matrix A satisfies the D-RIP condition 5k 〈 1/3 or 52k 〈 x/2/2, then all signals f with D＊f are k-sparse can be recovered exactly via the constrained l1 minimization based on y = A f, where D＊ is the conjugate transpose of a tight frame D. These bounds are sharp when D is an identity matrix, see Cai and Zhang＇s work. These bounds are greatly improved comparing to the condition 8k 〈 0.307 or 52k 〈 0.4931. Besides, if 3k 〈 1/3 or δ2k 〈 √2/2, the signals can also be stably reconstructed in the noisy cases.
