目的 针对目前基于稀疏表示的超分辨率重建算法中对字典原子的选取效率低、图像重建效果欠佳的问题，本文提出了核方法与一种高效的字典原子相关度筛选方法相融合的图像超分辨重建算法，充分利用字典原子与图像的相关度，选用对重建的贡献最大的原子来提高重建的效率和效果。 方法 首先，通过预处理高分辨率得
到高、低分辨率图像样本集，通过字典学习得到高、低分辨率字典对；然后，对字典原子进行非相关处理提高字典原子的表达能力；最后，利用低分辨率字典，引入核方法和字典原子筛选方法进行稀疏表示，求解稀疏表示问题得到稀疏表示系数，结合高分辨率字典重建出高分辨率图像。结果 实验结果表明：本文方法与对比方法相比，图像重建时间提高了28.5%；图像结构相似度提高了7.3%；峰值信噪比提高了1.77dB。原有的基于字典学习的方法对于字典选取具有一定的盲目性，所选取的原子与重建图像相关度较低，使重建效果差，本文的方法获得的字典原子可以减少稀疏表示过程的时耗，同时提高稀疏表示的精度。 结论 本文方法经实验证明，使图像的稀疏表示过程的重建时间明显减少，重建效果也有一定的提高，并且在训练样本较少的情况下同样有良好的重建效率和效果，适合在实际中使用。
Super resolution reconstruction algorithm based on kernel sparse representation and atomic correlation
Cheng Deqiang,Liu Weilong,Shao Lirong,Chen Liangliang(School of Information and Control Engineering,China University of Mining and Technology)
Objective In order to overcome the low efficiency of dictionary atom screening and the unsatisfactory results in some super-resolution methods based on sparse representation, this paper proposes a super-resolution reconstruction algorithm based on the combination of kernel method and dictionary atomic correlation, makes full use of the correlation between the dictionary and the image, and selects the atoms with the greatest contribution to the reconstruction to improve the efficiency and effect of the reconstruction. Method Firstly, a set of low-resolution and high-resolution samples is obtained by pre-processing applied on the high-resolution images, low-resolution and high-resolution dictionaries are learned by dictionary learning algorithm.Then,,the dictionary atom is uncorrelated to improve the ability of the dictionary atom to express. Finally, using the low resolution dictionary, the kernel method and the dictionary atom screening method are used for sparse representation, and sparse representation problem is solved to obtain sparse coefficients, and super-resolution image is recovered by these coefficients. Result The experimental results show that, compared with the contrast method, the image reconstruction time is increased by 28.5%, the image structure similarity is increased by 7.3%, and the peak signal-to-noise ratio is increased by 1.77dB. The original method based on dictionary learning for dictionary selection has a certain blindness, the atom and the reconstruction image correlation degree is low, the reconstruction effect is poor, this method can reduce the dictionary sparse representation of time consumption, and improve the accuracy of sparse representation. Conclusion This method has been proved by experiments that the reconstruction time of image sparse representation process is obviously reduced, the reconstruction effect is also improved, and it also has good reconstruction efficiency and effectiveness under the condition of fewer training samples, which is suitable for practical use.