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.

Key words: partial differential equation, blind denoising and deblurring, super-resolution reconstruction, variational method