【摘要】 提出一种基于偏微分方程的图像盲去模糊超分辨率重建算法，旨在未知模糊核的情况下，将含噪声的低分辨率模糊图像重建为清晰的高分辨率图像.首先，针对图像退化过程构建变分问题，并借助变分方法推导出偏微分方程模型.其次，结合交替方向法和数值差分方法，通过设计时空全离散数值格式求解未知的模糊核和清晰的图像.再次，通过一系列数值实验，分析参数选择对图像重建效果的影响，确定合适的参数设置.最后，针对若干遥感图像进行实验，实验结果证明了所给模型的有效性与可靠性.更多还原

【Abstract】 We proposed a blind image deblurring and super-resolution reconstruction algorithm based on partial differential equations(PDE). The goal was to reconstruct clear, high-resolution images from noisy, low-resolution blurred images without prior knowledge of the blur kernel. Firstly, we constructed a variational problem for the image degradation process and derived a PDE model by using variational methods. Secondly, by combining the alternating direction method and numerical difference method, we designed a spatiotemporal fully discrete numerical scheme to solve the unknown blur kernel and the clear image. Thirdly, through a series of numerical experiments, we analyzed the impact of parameter selection on image reconstruction performance and determined appropriate parameter settings. Finally, experiments were conducted on several remote sensing images, and the experimental results proved the effectiveness and reliability of the proposed model.更多还原