杨帅锋, 赵瑞珍. 基于低秩矩阵和字典学习的图像超分辨率重建[J]. 计算机研究与发展, 2016, 53(4): 884-891.
 引用本文: 杨帅锋, 赵瑞珍. 基于低秩矩阵和字典学习的图像超分辨率重建[J]. 计算机研究与发展, 2016, 53(4): 884-891.
Yang Shuaifeng, Zhao Ruizhen. Image Super-Resolution Reconstruction Based on Low-Rank Matrix and Dictionary Learning[J]. Journal of Computer Research and Development, 2016, 53(4): 884-891.
 Citation: Yang Shuaifeng, Zhao Ruizhen. Image Super-Resolution Reconstruction Based on Low-Rank Matrix and Dictionary Learning[J]. Journal of Computer Research and Development, 2016, 53(4): 884-891.

## Image Super-Resolution Reconstruction Based on Low-Rank Matrix and Dictionary Learning

• 摘要: 基于稀疏表示和字典学习的超分辨率重建算法没有对图像进行分解，直接将整幅图像的信息都进行了学习重建.由低秩矩阵理论知，可将图像分解成低秩部分和稀疏部分.根据图像各部分信息的特征分别用不同的方法进行超分辨率重建，将能更加有效地利用图像的特征.据此提出了一种基于低秩矩阵和字典学习的超分辨率重建方法.该方法首先通过对图像进行低秩分解得到图像的低秩部分和稀疏部分，图像的低秩部分保留了图像的大部分信息.算法只对图像的低秩部分通过字典学习的方法进行超分辨率重建，图像的稀疏部分则不参与学习重建，而是采用双三线性插值的方法进行重建.实验分析表明，图像的重建质量有所提升，同时减少了一定的重建时间，提升了算法的运行速度.与现有算法比较，在视觉效果、峰值信噪比、算法运行速度等方面均获得了更好的结果.

Abstract: Super-resolution (SR) reconstruction based on sparse representation and dictionary learning algorithm does not decompose the image at first. It reconstructs the image with its whole information based on sparse representation and dictionary learning algorithm directly. It is said that images can be decomposed into low-rank part and sparse part by low-rank matrix theory. Using different methods according to the characteristics of the different parts can be more effective to use the characteristics of the image. This paper proposes a super-resolution reconstruction method based on low-rank matrix and dictionary learning. The method obtains the low-rank part and sparse part of the original image via low-rank decomposition at first. The low-rank part retains most of the information of the image. The algorithm reconstructs the image based on dictionary learning method only for the low-rank part. The sparse part of the image reconstruction is not involved in the learning method, instead its reconstruction is based on linear interpolation method directly. Experimental results show that it can not only enhance the quality of the image reconstruction but also reduce the time of the reconstruction. Compared with existing algorithms, our method obtains better results in the visual effects, the peak signal to noise ratio and the running speed of the algorithm.

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