学术报告（李海洋 2025.6.6）

摘要：In this talk, we propose a class of tensor iterative thresholding algorithms, termed Tensor Band Restricted Thresholding (TBRT) algorithm, to address the Affine Tensor Rank Minimization (ATRM) problem. Compared to existing methods, our algorithm offers two significant differences: First, it avoids the use of non-convex functions to characterize tensor low-rankness. Second, it eliminates the need for tuning regularization parameters, a common requirement in most existing algorithms.Furthermore, we establish theoretical guarantees of our algorithms for the recovery of exact solutions to the ATRM problem under specific conditions, which rely on the Tensor Restricted Isometry Property (T-RIP). And we demonstrate that random measurement sets drawn from sub-Gaussian distributions can satisfy these conditions with high probability under appropriate sampling rates, which depend on the tubal rank and tensor dimensions. Finally, extensive numerical experiments have conducted to validate the effectiveness of our proposed sampling rates and the accuracy of the TBRT algorithm.