The single-image super-resolution (SISR) network based on deep learning is dedicated to learning the mapping between low-resolution (LR) images and high-resolution (HR) images. The optimal parameters of these networks often require extensive training on large-scale external image databases. For medical magnetic resonance (MR) images, there is a lack of large data sets containing high-quality images. Some deep networks that perform well on natural images cannot be fully trained on MR images, which limits the super-resolution (SR) performance. In traditional methods, the non-local self-similarity has been verified as useful statistical prior information for image restoration. The inherent feature correlation not only exists between pixels, but some patches also tend to be repeated at different positions within and across scales of MR images. Therefore, in this paper, we propose a mixed self-similarity attention network (MSAN) to explore the long-range dependencies of different regions fully. In the feature map of the entire input MR image, the prior information of self-similarity is divided into two scales: point-similarity and patch-similarity. We use points and patches that are highly similar to the current area to restore a more detailed structural texture. The internal correlation items can be used as an essential supplement to the limited external training dataset. Besides, the large number of less informative background in MR images will interfere with practical self-similarity information. A dual attention mechanism combining first-order attention and second-order attention gives more weight to salient features and suppresses the activation of useless features. Comprehensive experiments demonstrate that the proposed achieves significantly superior results on MR images SR while outperforming state-of-the-art methods by a large margin quantitatively and visually.
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