Abstract: The fast single image super-resolution via self-example learning and sparse representation makes the artifacts of reconstructed image obvious and the reconstruction efficiency low. This paper proposes a fast image super-resolution algorithm for residual dictionary learning to eliminate the artifacts and improve the reconstruction speed. The dictionary is trained by using a high frequency residual map based on an external image set, which reduces the complexity of dictionary training, enhances the representation ability of high-frequency information and eliminates the reconstructed artifacts. To solve the problem of high complexity of sparse representation, the orthogonal matching pursuit algorithm based on Cholesky decomposition is used to quickly obtain the sparse coefficients, and the high frequency residual dictionary is used to realize super-resolution reconstruction. The use of iterative back-projection further improves the reconstructed image quality, which greatly improves the efficiency of the algorithm and achieves better reconstructed image. The experiment results show that the proposed algorithm improves the peak signal to noise ratio and visual effect. Compared with the traditional algorithm, the proposed algorithm runs faster and gets the enhanced texture and better quality of reconstructed images.

Key words: super-resolution, high frequency residual dictionary, orthogonal matching pursuit algorithm, iterative back-projection

摘要： 针对基于自学习和稀疏表示的快速单图像超分辨率重建图像伪影明显、执行效率低的问题，提出了残差字典学习的快速图像超分辨率算法，以消除伪影，提高重建速度。通过采用基于外部图像集的高频残差图来训练字典，以降低字典训练的复杂度，并增强字典对高频信息的表达，消除重建伪影。同时，针对稀疏表示求解复杂度较高的问题，采用基于Cholesky分解的正交匹配追踪算法快速求解出稀疏系数，联合高频残差字典实现超分辨率重建，并对稀疏重建的高频图像使用迭代反投影进一步改善图像质量，极大地提高了算法的执行效率及图像重建效果。实验结果表明，该算法较传统算法在峰值信噪比和视觉效果上有所提升，运行速度快，重建图像的纹理特征和质量都得到了增强。

关键词: 超分辨率, 高频残差字典, 正交匹配追踪算法, 迭代反投影