The resolution of cameras is increasing, and speedup of various image processing is required to accompany this increase. A simple way of acceleration is processing the image at low resolution and then upsampling the result. Moreover, when we can use an additional high-resolution image as guidance formation for upsampling, we can upsample the image processing results more accurately. We propose an approach to accelerate various image processing by downsampling and joint upsampling. This paper utilizes per-pixel look-up tables (LUTs), named local LUT, which are given a low-resolution input image and output pair. Subsequently, we upsample the local LUT. We can then generate a high-resolution image only by referring to its local LUT. In our experimental results, we evaluated the proposed method on several image processing filters and applications: iterative bilateral filtering, ℓ0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _0$$\\end{document} smoothing, local Laplacian filtering, inpainting, and haze removing. The proposed method accelerates image processing with sufficient approximation accuracy, and the proposed outperforms the conventional approaches in the trade-off between accuracy and efficiency. Our code is available at https://fukushimalab.github.io/LLF/.