Analysis of the ratio of ℓ1 and ℓ2 norms in compressed sensing
Analysis of the ratio of ℓ1 and ℓ2 norms in compressed sensing
复制标题
压缩感知中≤1范数与≤2范数的比值分析
DOI：
10.1016/j.acha.2021.06.006
复制
发表时间：
2021
影响因子：
2.5
通讯作者：
Webster, Clayton G.
中科院分区：
文献类型：
--
作者：
Xu, Yiming;Narayan, Akil;Tran, Hoang;Webster, Clayton G.
我们研究了在压缩感知中作为稀疏性促进目标的101和102范数之比（101/102）。首先，我们提出了一个新的标准，保证了一个s-稀疏信号是局部极小值的目标，我们的标准是可解释的，在实践中有用。利用测量矩阵零空间的几何特征，给出了第一个一致恢复条件，并证明了这一条件对一类随机矩阵是成立的.我们还分析了噪声污染数据时该过程的鲁棒性。数值实验提供了在压缩感知中比较的一些其他流行的非凸方法的E11/E12。最后，我们提出了一种新的初始化方法来加速数值优化过程。我们称之为这种初始化方法支持选择，我们证明，它经验性地提高了现有的E101/E102算法的性能。
We study the ratio of ℓ 1 and ℓ 2 norms (ℓ 1/ℓ 2) as a sparsity-promoting objective in compressed sensing. We first propose a novel criterion that guarantees that an s-sparse signal is the local minimizer of the ℓ 1/ℓ 2 objective; our criterion is interpretable and useful in practice. We also give the first uniform recovery condition using a geometric characterization of the null space of the measurement matrix, and show that this condition is satisfied for a class of random matrices. We also present analysis on the robustness of the procedure when noise pollutes data. Numerical experiments are provided that compare ℓ 1/ℓ 2 with some other popular non-convex methods in compressed sensing. Finally, we propose a novel initialization approach to accelerate the numerical optimization procedure. We call this initialization approach support selection, and we demonstrate that it empirically improves the performance of existing ℓ 1/ℓ 2 algorithms.