Reconstruction of sparse signals via neurodynamic optimization

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Journal Article
International Journal of Machine Learning and Cybernetics, 2019, 10 (1), pp. 15 - 26
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© 2017, Springer-Verlag Berlin Heidelberg. 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.
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