The Dantzig selector: Recovery of Signal via ${\ell }_1-\alpha {\ell }_2$ Minimization

Abstract

In the paper, we proposed the Dantzig selector based on the ${\ell }_1-\alpha {\ell }_2$~$(0<\alpha \le 1)$ minimization for the signal recovery. In the Dantzig selector, the constraint $\Vert {\mathbf{A}}^{\top }(\mathbf{b}-\mathbf{A}\mathbf{x}){\Vert }_{\infty }\le \eta$ for some small constant $\eta >0$ means the columns of $\mathbf{A}$ has very weakly correlated with the error vector $\mathbf{e}=\mathbf{A}\mathbf{x}-\mathbf{b}$. First, recovery guarantees based on the restricted isometry property (RIP) are established for signals. Next, we propose the effective algorithm to solve the proposed Dantzig selector. Last, we illustrate the proposed model and algorithm by extensive numerical experiments for the recovery of signals in the cases of Gaussian, impulsive and uniform noise. And the performance of the proposed Dantzig selector is better than that of the existing methods.

References in corpus (8)

• Discussion: The Dantzig selector: Statistical estimation when $p$ is much larger than $n$
• Discussion: A tale of three cousins: Lasso, L2Boosting and Dantzig
• Discussion: The Dantzig selector: Statistical estimation when $p$ is much larger than $n$
• Discussion: The Dantzig selector: Statistical estimation when $p$ is much larger than $n$
• Discussion: The Dantzig selector: Statistical estimation when $p$ is much larger than $n$
• SNR Estimation in Linear Systems with Gaussian Matrices
• Generalized Dantzig Selector: Application to the k-support norm
• Discussion: The Dantzig selector: statistical estimation when $p$ is much larger than $n$

Cited by in corpus (3)

• Enhanced total variation minimization for stable image reconstruction
• Efficient Low Rank Matrix Recovery With Flexible Group Sparse Regularization
• An SDP Relaxation for the Sparse Integer Least Squares Problem