Title: LOSSLESS SINGLE IMAGE SUPER RESOLUTION FROM LOW-QUALITY JPG IMAGES. Abstract: Super Resolution (SR) is a fundamental and important low-level computer vision (CV) task. Different from traditional SR models, this study concentrates on a specific but realistic SR issue: How can we obtain satisfied SR results from compressed JPG (C-JPG) image, which widely exists on the Internet. In general, C-JPG can release storage space while keeping considerable quality in visual. However, further image processing operations, e.g., SR, will suffer from enlarging inner artificial details and result in unacceptable outputs. To address this problem, we propose a novel SR structure with two specifically designed components, as well as a cycle loss. In short, there are mainly three contributions to this paper. First, our research can generate high-qualified SR images for prevalent C-JPG images. Second, we propose a functional sub-model to recover information for C-JPG images, instead of the perspective of noise elimination in traditional SR approaches. Third, we further integrate cycle loss into SR solver to build a hybrid loss function for better SR generation. Experiments show that our approach achieves outstanding performance among state-of-the-art methods.