中文摘要：

针对基于稀疏重建的图像超分辨率（SR）算法一般需要外部训练样本,重建质量取决于待重建图像与训练样本的相似度的问题,提出一种基于局部回归模型的图像超分辨率重建算法。利用局部图像结构会在不同的图像尺度对应位置重复出现的事实,建立从低到高分辨率图像块的非线性映射函数一阶近似模型用于超分辨率重建。其中,非线性映射函数的先验模型是直接对输入图像及其低频带图像的对应位样本块对通过字典学习的方法得到。重建图像块时利用图像中的非局部自相似性,对多个非局部自相似块分别应用一阶回归模型,加权综合得到高分辨率图像块。实验结果表明,该算法重建的图像与同样利用图像具有自相似性的相关超分辨率算法相比,峰值信噪比（PSNR）平均提高0.3~1.1 d B,主观重建效果亦有明显提高。

英文摘要：

Image Super-Resolution（ SR） algorithms based on sparse reconstruction generally require external training samples. The shortcoming of these algorithms is that the reconstruction quality depends on the similarity between the image to be reconstructed and the training sample. In order to solve the problem,an image super-resolution reconstruction algorithm based on local regression model was proposed. Using the fact that the local image structure would repeat in the corresponding position of different image scales,a first-order approximation model of the nonlinear mapping function from low to high resolution image patches was built for super-resolution reconstruction. The prior model of the nonlinear mapping function was established by handling the in-place example pair of the input image and its low frequency band image with dictionary learning. During the reconstruction of the image block,the non-local self-similarity of image was used and the first-order regression model was applied to multiple non-local self-similarity patches respectively,the high-resolution image patch could be obtained through weighted summing. The experimental results show that,compared with other super-resolution algorithms which also make use of image self-similarity,the average Peak Signal-to-Noise Ratio（ PSNR） of the reconstructed images of the proposed algorithm is increased by 0. 3 ~ 1. 1 d B,and the subjective reconstruction effect of the proposed algorithm is improved significantly as well.