A distributed neurodynamic algorithm for sparse signal reconstruction via ℓ1-minimization

This paper proposes a distributed neurodynamic algorithm for sparse signal reconstruction by addressing ℓ1-minimization problems. Firstly, a ℓ1-minimization problem is transformed into a distributed model, drawing support from multi-agent consensus theory. Secondly, to address this distributed model, a novel distributed neurodynamic algorithm is proposed by employing derivative feedback and projection operator. It is proved that the proposed neurodynamic algorithm is globally convergent by utilizing the properties of projection operator and set-valued system. Moreover, compared with the existing distributed neurodynamic algorithms, the proposed neurodynamic algorithm is inverse-free and does not involve any matrix decomposition. Finally, some experimental results on sparse signal reconstruction indicate the effectiveness of the proposed neurodynamic algorithm.