摘要
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.
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.
基金
Supported by NSFC(Grant No.11171299)
