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Abstract The quality of solar images plays an important role in the analysis of small events in solar physics. Therefore, the improvement of image resolution based on super-resolution (SR) reconstruction technology has aroused the interest of many researchers. In this paper, an improved conditional denoising diffusion probability model (ICDDPM) based on the Markov chain is proposed for the SR reconstruction of solar images. This method reconstructs high-resolution (HR) images from low-resolution images by learning a reverse process that adds noise to HR images. To verify the effectiveness of the method, images from the Goode Solar Telescope at the Big Bear Solar Observatory and the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory are used to train a network, and the spatial resolution of reconstructed images is 4 times that of the original HMI images. The experimental results show that the performance based on ICDDPM is better than the previous work in subject judgment and object evaluation indexes. The reconstructed images of this method have higher subjective vision quality and better consistency with the HMI images. And the structural similarity and rms index results are also higher than the compared method, demonstrating the success of the resolution improvement using ICDDPM. 

Abstract In recent years, the new physics of the Sun has been revealed using advanced data with high spatial and temporal resolutions. The Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory has accumulated abundant observation data for the study of solar activity with sufficient cadence, but their spatial resolution (about 1″) is not enough to analyze the subarcsecond structure of the Sun. On the other hand, high-resolution observation from large-aperture ground-based telescopes, such as the 1.6 m Goode Solar Telescope (GST) at the Big Bear Solar Observatory, can achieve a much higher resolution on the order of 0.″1 (about 70 km). However, these high-resolution data only became available in the past 10 yr, with a limited time period during the day and with a very limited field of view. The Generative Adversarial Network (GAN) has greatly improved the perceptual quality of images in image translation tasks, and the self-attention mechanism can retrieve rich information from images. This paper uses HMI and GST images to construct a precisely aligned data set based on the scale-invariant feature transform algorithm and t0 reconstruct the HMI continuum images with four times better resolution. Neural networks based on the conditional GAN and self-attention mechanism are trained to restore the details of solar active regions and to predict the reconstruction error. The experimental results show that the reconstructed images are in good agreement with GST images, demonstrating the success of resolution improvement using machine learning.