基于自适应分数阶全变分的超分辨率图像重建

超分辨率图像重建在各领域有重要的应用价值，具有广阔的应用前景。超分辨率图像重建是一个病态求逆问题，最有效的解决方法是添加正则化项进行处理。本文在传统的全变分的基础上，添加分数阶全变分作为正则化项约束解空间，并利用纹理检测函数判断图像中不同位置的局部特征，自适应地选择其合适的阶次。采用交替方向乘子算法(ADMM)将优化函数划分为多个子问题进行求解，降低运算的复杂程度。本文全变分和自适应分数阶全变分的双正则化约束，在去除噪声锐化边缘的同时，根据图像的特征，自适应地重建出了纹理细节信息。实验结果表明，与其他方法相比，本文方法提高了图像的重建质量，且峰值信噪比（PSNR）和结构相似度（SSIM）值都有一定提高。

Super-resolution Image Reconstruction Based on Adaptive FractionalOrder Total Variation Regularization

 Super-resolution image reconstruction has important application value in various fields and has broad application prospects. It is an ill-posed problem to reconstruct the high-resolution image from the low-resolution image. The most effective method is to add the regularization term to solve it. This paper adds the fractional order total variation (FOTV) as the regularization term constraint solution space based on the traditional total variation (TV), and uses the texture detection function to determine the local features at different locations in the image, and selects the adaptive order. The alternating direction multiplier algorithm is used to divide the optimization function into multiple sub-problems and reduce the complexity of the operation. In this paper, the bi-regularization constraints of TV and the adaptive FOTV are used to adaptively reconstruct the texture detail information while removing the noise and sharpening edge. Experimental results show that compared with other methods, the proposed method improves the quality of image reconstruction, and both the PSNR and SSIM values are improved.