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In this article, a new projection neural network (PNN) for solving L₁-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
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