论文标题
提起的$ \ ell_1 $稀疏恢复框架
A Lifted $\ell_1 $ Framework for Sparse Recovery
论文作者
论文摘要
由重新加权的$ \ ell_1 $用于稀疏恢复的方法，我们提出了一个提起的$ \ ell_1 $（ll1）正则化，这是文献中几种流行正规化的广义形式。通过探索此类连接，我们发现有两种类型的提升功能可以保证所提出的方法等效于$ \ ell_0 $最小化。在计算上，我们通过乘数（ADMM）的交替方向方法设计有效的算法，并为不受约束的公式建立收敛性。提出了实验结果，以证明这种概括如何改善对最新的稀疏恢复。
Motivated by re-weighted $\ell_1$ approaches for sparse recovery, we propose a lifted $\ell_1$ (LL1) regularization which is a generalized form of several popular regularizations in the literature. By exploring such connections, we discover there are two types of lifting functions which can guarantee that the proposed approach is equivalent to the $\ell_0$ minimization. Computationally, we design an efficient algorithm via the alternating direction method of multiplier (ADMM) and establish the convergence for an unconstrained formulation. Experimental results are presented to demonstrate how this generalization improves sparse recovery over the state-of-the-art.
