A Continuous-Time Recurrent Neural Network for Sparse Signal Reconstruction Via ℓ1 Minimization

This paper presents a neurodynamic model for solving e1 minimization problems for sparse signal reconstruction. The essence of the proposed approach lies in its capability to operate in continuous time, which enables it to outperform most existing iterative e1 -solvers in dynamic environments. The model is described by a goal-seeking recurrent neural network and it evolves according to its deterministic neurodynamics. It is proved that the model globally converges to the optimal solution to the e1 -minimization problem under study. The connection weights of the neural network model are determined by using subgradient projection methods and the activation function is designed based on subdifferential. Due to its simple structure, the hardware implementation of this neurodynamic model is viable and cost-effective, which sheds light on real-time sparse signal recovery via large scale e1 minimization formulations.