Journal
NEURAL NETWORKS
Volume 122, Issue -, Pages 40-53Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.neunet.2019.10.006
Keywords
Neural network; l(1)-norm minimization; l(p)-norm (2 >= p >= 1); Smoothing approximation
Funding
- Fundamental Research Funds for the Central Universities [XDJK2019B010]
- Natural Science Foundation of China [61773320]
- Natural Science Foundation Project of Chongqing CSTC [cstc2018jcyjAX0583, cstc2018jcyjAX0810]
- Research Foundation of Key laboratory of Machine Perception and Children's Intelligence Development - CQUE, China [16xjpt07]
- Foundation of Chongqing University of Education [KY201702A]
- Qatar National Research Fund (a member of Qatar Foundation) [NPRP 7-1482-1-278]
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This paper investigates a smoothing neural network (SNN) to solve a robust sparse signal reconstruction in compressed sensing (CS), where the objective function is nonsmooth l(1)-norm and the feasible set satisfies an inequality of l(p)-norm (2 >= p >= 1) which is used for measuring residual errors. With a smoothing approximate technique, the non-smooth and non-Lipschitz continuous issues of the l(1)-norm and the gradient of l(p)-norm can be solved efficiently. We propose a SNN which is modeled by a differential equation and give its circuit implementation. In this case, we prove the proposed SNN converges to the optimal of considered problem. Simulation results are discussed to demonstrate the efficiency of the proposed algorithm. (c) 2019 Elsevier Ltd. All rights reserved.
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