Recent research on image restoration have achieved great success with the aid of deep learning technologies, but, many of them are limited to dealing SR with realistic settings. To alleviate this problem, we introduce a new formulation for image super-resolution to solve arbitrary scale image super-resolution methods. Based on the proposed new SR formulation, we can not only super-resolve images with multiple scales, but also find a new way to analyze the performance of super-resolving process. We demonstrate that the proposed method can generate high-quality images unlike conventional SR methods.