Reconstruction of sparse signals via neurodynamic optimization

It is significant to solve \(l_1\) minimization problems efficiently and reliably in compressed sensing (CS) since the \(l_1\) minimization is essential for the recovery of sparse signals. In view of this, a neurodynamic optimization approach is proposed for solving the \(l_1\)-minimization problems for reconstruction of sparse signals based on a projection neural network (PNN). The proposed neurodynamic optimization approach differs from most \(l_1\)-solvers in that it operates in continuous time rather than being specified by discrete iterations; i.e., it evolves according to deterministic neurodynamics. The proposed PNN is designed based on subgradient projection methods. The neural network has a simple structure, giving it a potential to be implemented as a large-scale analog circuit. It is proved that under appropriate conditions on the measurement matrix, every neuronal state of the proposed neural network is convergent to the optimal solution of the \(l_1\)-minimization problem under study. Simulation results are provided to substantiate the effectiveness of the proposed approach.