Centralized and Collective Neurodynamic Optimization Approaches for Sparse Signal Reconstruction via L1-Minimization

You Zhao, Xiaofeng Liao, Xing He

Abstract:

This article develops several centralized and collective neurodynamic approaches for sparse signal reconstruction
by solving the L1-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 L1-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 L1-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.