Analysis Recovery With Coherent Frames and Correlated Measurements

作者：Xia, Yu; Li, Song^*

来源：IEEE Transactions on Information Theory, 2016, 62(11): 6493-6507.

DOI：10.1109/TIT.2016.2606638

• l(1)-analysis
• restricted eigenvalue condition
• correlated matrices
• Dantzig selector
• LASSO
• robust NullSpace property

This paper introduces the restricted eigenvalue condition adapted to frame D (D-RE), which is a natural extension to the standard restricted eigenvalue condition. The D-RE condition is a relaxation of the D-dagger+-RIP, where D-dagger = (DD*)-(1) D is the canonical dual frame of D. We establish the D-RE condition for several classes of correlated measurement matrices, when the covariance matrix of row measurements satisfies the D-RE condition. Furthermore, by the D-RE condition, we get the error bounds in the analysis LASSO (ALASSO) and the analysis Dantzig Selector (ADS) under a sparsity scenario. In order to recover non-sparse signals, we consider the robust l(2) D-nullspace property of correlated Gaussian matrices. Similarly, we get the error estimations in the ALASSO and the ADS in non-sparse case. The approximation equivalence between the ALASSO and the ADS is also established by calculating prediction loss difference.

• 出版日期2016-11
• 单位浙江大学