中文摘要：

目的 大多数图像内插方法只考虑低分辨率图像的下采样降质过程,忽略编码噪声的影响.提出一种新的自适应对称自回归模型的压缩图像内插方法.方法 假设局部图像相似的图像块具有相同的图像内插模型.方法分为训练和重建两个阶段.在训练阶段,首先对训练图像采用主成分分析提取图像块的局部梯度主方向,根据方向进行一次分类,分别建立各个方向的对称自回归模型和训练集;其次对每个方向的训练集,根据图像基元特征,利用K均值聚类方法进行二次分类;最后对每个二次分类训练子集,选择其所属方向类的模型,使用有约束的最小二乘法估计对应于该子集的模型系数.在重建阶段,首先根据测试图像块的局部梯度主方向,确定方向类别,再计算测试块基元特征和该方向类中所有聚类中心的欧氏距离,选择具有最小欧氏距离的聚类中心的自回归模型用于内插.结果 采用8种不同的测试图像在JPEG的2种量化方式条件下进行测试,与7种典型的图像内插相比,结果表明本文方法能够有效地克服编码噪声的影响,峰值信噪比（PSNR）和结构相似度（SSIM）均优于其他方法.结论 本文方法具有较低的复杂度,可以适用于图像通信中增强图像的分辨率.

英文摘要：

Objective Most image interpolations only consider the quality degradation of low-resolution images by down sampling without accounting for quantization noise.We propose a novel compression image interpolation method using adaptive symmetrical autoregressive models in this paper.Method Blocks with similar local images are assumed to have the same interpolation model.The proposed method has two phases：training and reconstruction.In the training phase,the local gradient direction is first obtained via principal component analysis （PCA） to classify all training blocks into four directions and to build the corresponding symmetrical autoregressive models and training sets for every direction.Second,the training sets for every direction are classified into subclasses according to the basic features of the K-means clustering algorithm.Finally,the model of the direction to which each subclass belongs is chosen,and the constrained least square method is used to estimate the weights of the model.In the reconstruction phase,the direction of the pixel is first determined according to the local gradient direction of the neighboring pixel.Subsequently,by computing for the Euclidean distance between local primitive features and every clustering center in the selected direction,the model of each subclass with the least distance is chosen for interpolation.Results The eight test images and two quantization parameters of JPEG still image compression are used in the tests.Results show that the proposed method is better than other interpolations on the PSNR and SSIM,even in the presence of serious quantization noise.Conclusion The results demonstrate that the proposed method produces better results than other interpolations for both quantitative and visual comparisons and has low computational complexity.