As an important theory of sparse signal recovery, Compressive Sensing (CS) optimization methods usually produce good performance when the signal is sparse in some transform domains. In recent years, many methods that combining deep learning with traditional iterative optimization algorithms have been proposed and achieved exciting performance in the field of sparse signal recovery. In this paper, inspired by the Primal-Dual algorithm, we first transform the CS model into a saddle point problem,

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... and then propose a novel Learned Primal-Dual Network, called LPD-Net. The proposed LPD-Net explores the special structure of the 1 -norm regularization term and converts the original problem into two sub-problems that are easy to solve. Moreover, we also present a transformed sigmoid function to improve the performance of the proposed network. Experimental results demonstrate that the proposed LPD-Net outperforms other existing state-of-the-art methods for image CS reconstruction tasks. The demo-code of our LPD-Net method is available at: https://github.com/clzhang97/LPD-Net_pytorch.