Distributed Inertial Proximal Neurodynamic Approach for Sparse Recovery on Directed Networks

You Zhao, Xing He, Mingliang Zhou, Junzhi Yu, Tingwen Huang

Abstract:

This article investigates a fully distributed inertial
neurodynamic approach for sparse recovery. The approach is
based on proximal operators and inertia items. It aims to solve
the L1-norm minimization problem with consensus and linear
observation constraints over directed communication networks.
The proposed neurodynamic approach has the advantages of only
requiring the communication network to be directed and weightbalanced, does not involve a central processing node and global
parameters, which means that no single node can access the entire
network and observe it at any time, so it is fully distributed. To
effectively deal with the nonsmooth objective function, L1-norm,
the proximal operator method is used here. For efficiently
handling linear observation and consensus constraints, a primaldual method is applied to the inertial dynamic system. With the
aid of maximal monotone operator theory and Baillon–Haddad
lemmas, it reveals that the trajectories of our approach can
converge to consensus solution at the optimal solution, provided
that the distributed parameters satisfy technical conditions. In
addition, we aim to demonstrate the weak convergence of the
trajectories in our proposed neurodynamic approach toward the
zeros of the optimal operator in Hilbert space, using Opial’s
lemma. Finally, comparative experiments on sparse signal and
image recovery confirm the efficiency and effectiveness of our
proposed neurodynamic approach.