## 1 Introduction  
Super-resolution improved image resolution and enhanced the accuracy of image processing tasks such as target detection, semantic segmentation, and scene classification [1; 2; 3]. Applying super resolution to remote sensing could provide high-resolution datasets [4; 5; 6; 7; 8] for land planning, environmental protection, and disaster prediction [9; 10; 11]. In recent years, an increasing number of remote sensing satellites have been launched into orbit, and the imaging resolution of remote sensing satellites has been rising. This provides a wealth of training data for the super resolution of remote sensing images. Since deep networks were introduced to super-resolution techniques, various methods based on different backbone networks have been proposed one after another [12; 13; 14; 15; 16]. In these studies, several authors discussed the ill-posedness of super resolution [17; 18; 19; 20]. The same low-resolution image can be obtained by downsampling several different high-resolution images. As an inverse process of downsampling, super resolution predicts multiple high-resolution images from the same one low-resolution image and selects the high-resolution image that is most similar to the ground truth. Therefore, super resolution is an ill-posed problem. The space of all possible functions for mapping from a low-resolution image to high-resolution images is large. This poses difficulties in training super-resolution networks and limits the network's performance improvement. Consequently, reducing the ill-posedness of super resolution has become a significant research issue in the development of this technique. The VDSR-based super-resolution method [17] was one of the first proposed to reduce the ill-posedness of super resolution. In [17], it was noted that the limited number of layers in the feature extraction module of SRCNN restricted detail recovery in super-resolution output. VDSR effectively improved super-resolution performance by deepening the network to expand the receptive field. However, the number of layers in the current deep network is generally large, and the transformer structure further expands the receptive field of feature extraction. Therefore, simply deepening the network no longer reduces the ill-posedness of super resolution. In [20], the ill-posedness of super resolution was analyzed mathematically. The large space of possible functions for mapping from low-resolution images to high-resolution images makes it difficult to accurately fit a mapping function using a deep network. To increase the constraints of super-resolution networks, a dual regression network was proposed. This network introduced additional supervision during training by comparing super-resolution results with high-resolution ground truth and computing a loss function between the downsampled result image and the input image. This method effectively reduced the space of possible mapping functions. The dual regression network increased the number of supervisions from one to two, which increased the constraints in the super-resolution process and reduced the ill-posedness of super resolution. However, the second supervision was applied to the downsampled output image, potentially losing the recovered image detail again during the downsampling process. Moreover, the loss function computed between low-resolution images might be unsuitable for evaluating the super-resolution performance of the network. To further reduce the ill-posedness of super resolution, a Prediction-to-Prediction Super-Resolution (P2P-SR) network under a multi-level supervision paradigm was proposed. Unlike the conventional one-step or dual regression super resolution, our method utilized multiple Basic Super-Resolution Components (BSRC) with smaller scale factors for image reconstruction. Supervisions were applied at the output of each component, introducing multiple levels of constraints to the super-resolution process.