一种高效的基于Dai-Yuan投影的方法,用于信号恢复
Jamilu Sabi'u1, Ado Balili1, Homan Emadifar2,3,4
1Department of Mathematics, Faculty of Science, Yusuf Maitama Sule University, Kano, Nigeria.
PloS one
|June 10, 2024
概括
这项研究引入了一种改进的Dai-Yuan结合梯度 (CG) 方法,以克服数值干扰问题. 改进的算法有效地解决非线性受约束的单调系统,并在压缩传感应用中表现出强大的性能.
科学领域:
- 数字分析和优化 数字分析和优化
- 应用数学 应用数学 应用数学
- 信号处理 信号处理
背景情况:
- 经典的Dai-Yuan结合梯度 (CG) 方法,虽然在Lipschitz条件下具有全球收属性,并满足Wolfe线索搜索的下降条件,但由于干扰问题而存在数值性能问题.
- 当前的CG算法在应用于复杂系统时,往往在效率和稳定性方面扎,因此需要为实际应用进行改进.
研究的目的:
- 开发一种高效的Dai-Yuan CG算法的变体,能够解决非线性受约束单调系统 (NCMS).
- 解决和解决与原始的戴元CG方法固有的数值干扰问题.
- 为了证明拟议变体在压缩传感 (CS) 问题中的数值稳定性和适用性.
主要方法:
- 开发一个修改的Dai-Yuan结合梯度算法.
- 理论分析确保在利普希茨条件下的全球收和足够的下降要求,独立于线路搜索方法.
- 从文献中与现有的算法进行数值比较.
- 变体算法的应用在压缩传感 (CS) 中稀疏信号重建.
主要成果:
- 拟议的变量算法保持全球收属性,类似于未经修改的戴方法,当满足利普希茨和足够的下降条件时.
- 数值计算表明,变体算法比现有方法更强大,有效地克服了干扰问题.
- 该算法成功地重建了压缩传感 (CS) 场景中的稀疏信号,展示了其实际实用性.
结论:
- 戴元CG算法的高效变体为非线性受约束单调系统提供了强大的和数值稳定的解决方案.
- 这种增强的方法克服了原始算法的局限性,在数值计算中提供了更好的性能.
- 变种算法显示出在解决具有挑战性的问题上有效应用的承诺,例如压缩传感中的稀疏信号重建.
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