1. Analysis of the ratio of ℓ1 and ℓ2 norms for signal recovery with partial support information.
- Author
-
Ge, Huanmin, Chen, Wengu, and Ng, Michael K
- Subjects
ORTHOGONAL matching pursuit ,RESTRICTED isometry property ,RATIO analysis ,LENGTH measurement ,SIGNAL reconstruction - Abstract
The ratio of |$\ell _{1}$| and |$\ell _{2}$| norms, denoted as |$\ell _{1}/\ell _{2}$| , has presented prominent performance in promoting sparsity. By adding partial support information to the standard |$\ell _{1}/\ell _{2}$| minimization, in this paper, we introduce a novel model, i.e. the weighted |$\ell _{1}/\ell _{2}$| minimization, to recover sparse signals from the linear measurements. The restricted isometry property based conditions for sparse signal recovery in both noiseless and noisy cases through the weighted |$\ell _{1}/\ell _{2}$| minimization are established. And we show that the proposed conditions are weaker than the analogous conditions for standard |$\ell _{1}/\ell _{2}$| minimization when the accuracy of the partial support information is at least |$50\%$|. Moreover, we develop effective algorithms and illustrate our results via extensive numerical experiments on synthetic data in both noiseless and noisy cases. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF