In recent years, tensor-based methods for high-dimensional image processing have been extensively applied in fields such as computer vision, medical imaging, science and engineering, and remote sensing, achieving significant accomplishments. However, when dealing with large-scale high-dimensional image, existing tensor modeling and computational methods suffer from issues such as inadequate data representation, low computational efficiency, high memory consumption, and limited flexibility. To address these problems, fast randomized algorithms for large-scale image compression and representation have been studied within popular and effective high-order tensor frameworks (e.g., T-SVD, Tucker, FCTN), leveraging sketching techniques from the field of randomized numerical algebra. The proposed methods can be applied to a range of high-dimensional image processing tasks, including MRI/CT reconstruction, color image and video inpainting, hyperspectral image denoising, hyperspectral anomaly detection, and surveillance video background subtraction. Experimental results demonstrate that our methods outperform current competitive approaches in both quantitative metrics and visual effects.