Due to the important application value of image super-resolution, many image super-resolution algorithms have been proposed in recent years. However, many single-image super-resolution algorithms usually have their own limitations and cannot achieve ideal results. To this end, this paper proposes a new single-image super-resolution method that uses non-local self-similarity, cross-resolution similarity, and global structure sparsity without relying on external instances. First, we obtain the initial high-resolution image through feature-constrained polynomial interpolation. Then, we use a database built by the input image to perform cross-resolution learning to predict the missing high-frequency information in the image. Finally, we use the residual filtering proposed in this paper to remove the noise introduced during interpolation and cross-resolution learning. Our method can be combined with other image super-resolution algorithms. Through extensive comparison experiments to verify, our method achieves higher numerical accuracy and pleasing visual effects.

由于图像超分辨率的重要应用价值，近年来提出了许多图像超分辨率算法。然而，许多单图像超分辨率算法通常都有其自身的局限性，无法达到理想的效果。为此，本文提出了一种新的单图像超分辨率方法，该方法利用非局部自相似性、交叉分辨率相似性和全局结构稀疏性，而不依赖外部实例。首先，我们通过特征约束多项式插值获得初始高分辨率图像。然后，我们使用由输入图像构建的数据库进行跨分辨率学习来预测图像中缺失的高频信息。最后，我们使用本文提出的残差滤波来去除插值和跨分辨率学习过程中引入的噪声。我们的方法可以与其他图像超分辨率算法相结合。通过大量的对比实验来验证，我们的方法实现了更高的数值精度和令人愉悦的视觉效果。