学术报告（王建军 2025.6.6）

摘要：In recent years, tensor-based methods for high-dimensional data processing have been extensively applied in fields such as image processing, computer vision, medical imaging, and remote sensing, achieving significant accomplishments. However, when dealing with large-scale high-dimensional data, 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 high-order tensor compression and representation have been studied within popular and effective tensor frameworks (e.g., T-SVD, Tucker, FCTN), leveraging sketching techniques from the field of randomized numerical algebra. Furthermore, advanced techniques such as non-convex regularization, gradient maps modeling, and  intrinsic tensor decomposition  have been employed to develop fast  and accurate high-order tensor recovery methods. Theoretically, we provide theoretical error bound analysis for the proposed approximation algorithms and convergence analysis for the recovery algorithms. The proposed methods can be applied to a range of high-dimensional data processing tasks, including medical image reconstruction, color image and video inpainting, 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.