In this paper, a simple and effective image-magnification algorithm based on intervals is proposed. A low-resolution image is magnified to form a high-resolution image using a block-expanding method. Our proposed method associates each pixel with an interval obtained by a weighted aggregation of the pixels in its neighborhood. From the interval and with a linear Kα operator, we obtain the magnified image. Experimental results show that our algorithm provides a magnified image with better quality (peak signal-to-noise ratio) than several existing methods.