In this paper, we introduce a novel method to reduce image to a small size, such that the quality of the image is improved when it is up-scaled. Recent hardwares including cameras and display devices allow us to capture and display high-resolution images. However, it is not always realistic to store and transmit those high-resolution images due to limitation of storage and network bandwidth. Therefore, high-resolution images are often down-scaled to be stored and transmitted, and then up-scaled back for display. To improve final image quality in this scenario, we first formulate selected up-scale methods as linear transformations. The optimal reduction methods are obtained as its inverse transformation. Based on this basic idea, we develop down-scale kernel that is optimized for each up-scale method. In our experiment, the proposed method could improve the quality of the up-scaled image noticeable.