In this article, a new projection neural network (PNN) for solving ${L_{\mathrm{1}}}$ -minimization problem is proposed, which is based on classic PNN and sliding mode control technique. Furthermore, the proposed network can be used to make sparse signal reconstruction and image reconstruction. First, a sign function is introduced into the PNN model to design fixed-time PNN (FPNN). Then, under the condition that the projection matrix satisfies the restricted isometry property (RIP), the stability and fixed-time convergence of the proposed FPNN are proved by the Lyapunov method. Finally, based on the experimental results of signal simulation and image reconstruction, the proposed FPNN shows the effectiveness and superiority compared with that of the existing PNNs.

中文翻译：

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求解L钪最小化问题的固定时间投影神经网络


在本文中，基于经典 PNN 和滑模控制技术，提出了一种用于解决 ${L_{\mathrm{1}}}$ 最小化问题的新投影神经网络（PNN）。此外，所提出的网络可用于进行稀疏信号重建和图像重建。首先，在 PNN 模型中引入符号函数来设计固定时间 PNN（FPNN）。然后，在投影矩阵满足受限等距性质（RIP）的条件下，通过Lyapunov方法证明了所提出的FPNN的稳定性和固定时间收敛性。最后，基于信号模拟和图像重建的实验结果，所提出的FPNN与现有的PNN相比显示了有效性和优越性。