This article develops several centralized and collective neurodynamic approaches for sparse signal reconstruction by solving the L1L_{1} -minimization problem. First, two centralized neurodynamic approaches are designed based on the augmented Lagrange method and the Lagrange method with derivative feedback and projection operator. Then, the optimality and global convergence of them are derived. In addition, considering that the collective neurodynamic approaches have the function of information protection and distributed information processing, first, under mild conditions, we transform the L1L_{1} -minimization problem into two network optimization problems. Later, two collective neurodynamic approaches based on the above centralized neurodynamic approaches and multiagent consensus theory are proposed to address the obtained network optimization problems. As far as we know, this is the first attempt to use the collective neurodynamic approaches to deal with the L1L_{1} -minimization problem in a distributed manner. Finally, several comparative experiments on sparse signal and image reconstruction demonstrate that our proposed centralized and collective neurodynamic approaches are efficient and effective.

中文翻译：

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通过 L钪最小化稀疏信号重建的集中和集体神经动力学优化方法


本文通过解决 L1L_{1} 最小化问题，开发了几种用于稀疏信号重建的集中式和集体神经动力学方法。首先，基于增强拉格朗日方法和带有导数反馈和投影算子的拉格朗日方法设计了两种集中式神经动力学方法。然后推导出它们的最优性和全局收敛性。此外，考虑到集体神经动力学方法具有信息保护和分布式信息处理的功能，首先，在温和条件下，我们将L1L_{1}最小化问题转化为两个网络优化问题。随后，基于上述集中式神经动力学方法和多智能体共识理论，提出了两种集体神经动力学方法来解决所获得的网络优化问题。据我们所知，这是首次尝试使用集体神经动力学方法以分布式方式处理 L1L_{1} 最小化问题。最后，关于稀疏信号和图像重建的几个比较实验表明，我们提出的集中式和集体神经动力学方法是高效且有效的。