The basins of attraction of the global minimizers of the non-convex sparse spike estimation problem
The basins of attraction of the global minimizers of the non-convex sparse spike estimation problem
复制标题
非凸稀疏尖峰估计问题的全局极小值的吸引力盆地
DOI：
10.1088/1361-6420/ab5aa3
复制
发表时间：
2018
期刊：
影响因子：
2.1
通讯作者：
Jean
中科院分区：
文献类型：
--
作者：
Y. Traonmilin;Jean
稀疏尖峰估计问题在于根据不确定的线性测量来估计许多离网脉冲源。信息论结果确保非凸函数的最小化能够恢复充分选择的测量（确定性或随机）的尖峰。为了解决这个问题，人们提出了受使用凸规划的有限维稀疏估计情况启发的方法。贪心启发法也显示出了很好的实际效果。然而，人们对理想的非凸最小化方法知之甚少。在本文中，我们研究了该非凸函数的全局最小值的形状：我们给出了全局最小值的显式吸引盆，表明随着测量数量的增加，非凸问题变得更容易。这对于涉及下降算法（例如贪婪启发式）的方法具有重要影响，并且它为此类下降方法的潜在改进提供了见解。
The sparse spike estimation problem consists in estimating a number of off-the-grid impulsive sources from under-determined linear measurements. Information theoretic results ensure that the minimization of a non-convex functional is able to recover the spikes for adequately chosen measurements (deterministic or random). To solve this problem, methods inspired from the case of finite dimensional sparse estimation where a convex program is used have been proposed. Also greedy heuristics have shown nice practical results. However, little is known on the ideal non-convex minimization method. In this article, we study the shape of the global minimum of this non-convex functional: we give an explicit basin of attraction of the global minimum that shows that the non-convex problem becomes easier as the number of measurements grows. This has important consequences for methods involving descent algorithms (such as the greedy heuristic) and it gives insights for potential improvements of such descent methods.
影响因子：
4.300
作者：
Hagar Ibrahim Labouta;Labiba K. El-Khordagui
通讯作者：
Labiba K. El-Khordagui