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Generative Adversarial Networks (GANs) are powerful tools for reconstructing Compressed Sensing Magnetic Resonance Imaging (CS-MRI). However most recent works lack exploration of structure information of MRI images that is crucial for clinical diagnosis. To tackle this problem, we propose the Structure-Enhanced GAN (SEGAN) that aims at restoring structure information at both local and global scale. SEGAN defines a new structure regularization called Patch Correlation Regularization (PCR) which allows for efficient extraction of structure information. In addition, to further enhance the ability to uncover structure information, we propose a novel generator SU-Net by incorporating multiple-scale convolution filters into each layer. Besides, we theoretically analyze the convergence of stochastic factors contained in training process. Experimental results show that SEGAN is able to learn target structure information and achieves state-of-theart performance for CS-MRI reconstruction.