Screen content has become one of the prominent mediums in the increasingly connected world. With the prevalence of remote collaboration and communication such as virtual conferences and online education, recent years have witnessed a dramatic increase in the data volume of the screen content. Screen content compression serves as the fundamental technology in fostering the storage, transmission, and exhibition of screen content. In this article, we target the super-resolution of the compressed screen content images, intending to tackle the real-world challenge problems. A dataset is proposed for the super-resolution of the screen contents contaminated with different compression distortion levels. Subsequently, we introduce the principle of the multi-hypothesis into the super resolution and propose a new paradigm for the restoration of the compressed screen content images. The luminance and sharpness similarity metric is adopted in the network learning to better adapt to the screen content characteristic and ensure perceptual fidelity. Experimental results verify the superiority and effectiveness of the proposed method.