Abstract: In image reconstruction, making full use of low-resolution images and estimation prior is an important issue. This paper proposes a novel algorithm, using R-filters method, through calculating the high-level information of image and building prior term. At the same time, it takes advantage of the Generalized Cross-Validation（GCV） to solve adaptive regularization parameter, strengthens adaptivity of the algorithm. Result shows that compared to the current main reconstruction algorithm（BTV, Sparse, Huber）, the Peak Signal-to-Noise Ratio（PSNR） of images is higher than others and details are also richer, also from the construction it shows R-filter is superior than others.

Key words: image reconstruction, R-filters, Generalized Cross Validation（GCV）, adaptive parameter, prior, Peak Signal-to-Noise Ratio（PSNR）

摘要： 针对图像重建中低分辨率图像信息的利用和先验项（正则化项）的估计问题，提出一种新颖的算法——R-滤子方法，通过计算输入图像的高阶信息来构建先验项，同时采用广义交叉验证（Generalized Cross Validation，GCV）方法自适应求解先验项参数（正则化参数），加强算法的自适应性。实验结果表明：重建图像的峰值信噪比值（Peak Signal-to-Noise Ratio，PSNR）比目前主要先验项方法（BTV、Sparse、Huber）的重建图像的值更高，从重建图像的局部细节和纹理也看出该方法的重建图像具有更丰富的信息，同时，从构造方法上说明R-滤子方法在计算上要优于其他方法。

关键词: 图像重建, R-滤子, 广义交叉验证（GCV）, 自适应参数, 先验项, 峰值信噪比值（PSNR）