Distributed Computation for Sparse Recovery via Continuous-Time Neurodynamic Approach

You Zhao, Xiaofeng Liao, Mingliang Zhou, Xing He

Abstract:

Sparsity has been extensively employed in
multimedia sensing and computing in consumer electronics,
signal and image processing, depth video codec, adaptive
sparse-type equalizer, blind speech separation, and machine
learning. Throughout this paper, we propose a novel distributed
projection neurodynamic approach for solving the Basis Pursuit
(BP) with flexible partition methods in a distributed manner.
The proposed neurodynamic approach requires only that the
network is undirected and connected, and no node can access the
entire matrix simultaneously. First, we equivalently formulate
the BP into a standard distributed optimization problem with a
flexible partition-by-blocks method to obtain global information,
and discuss the equivalence of their optimality conditions.
Then, we propose a distributed continuous-time neurodynamic
approach on the basis of primal-dual dynamical systems and
projection operators, and also study its global convergence
property. Finally, numerical experiments on sparse signals and
image recovery further verify the effectiveness and superiority
of our proposed neurodynamic approach.