| مستخلص: |
In this paper, we consider to recover a signal which is sparse in terms of a tight frame from undersampled measurements via -minimization problem for . In [Compressed sensing with coherent tight frames via -minimization for , Inverse Probl. Imaging 8 (2014) 761-777], Li and Lin proved that when there exists a , depending on such that for any , each solution of the -minimization problem can approximate the true signal well. The constant is referred to as the -RIP constant of order which was first introduced by Candès et al. in [Compressed sensing with coherent and redundant dictionaries, Appl. Comput. Harmon. Anal. 31 (2011) 59-73]. The main aim of this paper is to give the closed-form expression of . We show that for every -RIP constant , if where then the -minimization problem can reconstruct the true signal approximately well. Our main results also hold for the complex case, i.e. the measurement matrix, the tight frame and the signal are all in the complex domain. It should be noted that the-RIP condition is independent of the coherence of the tight frame (see [Compressed sensing with coherent and redundant dictionaries, Appl. Comput. Harmon. Anal. 31 (2011) 59-73]). In particular, when the tight frame reduces to an identity matrix or an orthonormal matrix, the conclusions in our paper coincide with the results appeared in [Stable recovery of sparse signals via -minimization, Appl. Comput. Harmon. Anal. 38 (2015) 161-176]. [ABSTRACT FROM AUTHOR] |
