Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank Approximation

作     者：Qin, Wenjin Wang, Hailin Zhang, Feng Ma, Weijun Wang, Jianjun Huang, Tingwen 

作者机构：Southwest Univ Sch Math & Stat Chongqing 400715 Peoples R China Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Peoples R China Ningxia Univ Sch Informat Engn Yinchuan 750021 Peoples R China Southwest Univ Sch Math & Stat Chongqing 400715 Peoples R China Southwest Univ Res Inst Intelligent Finance & Digital Econ Chongqing 400715 Peoples R China Texas A&M Univ Qatar Dept Math Doha Qatar 

出 版 物：《IEEE TRANSACTIONS ON IMAGE PROCESSING》 (IEEE Trans Image Process)

年 卷 期：2024年第33卷

页      面：2835-2850页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：National Key Research and Development Program of China 

主　　题：High-order T-SVD framework robust high-order tensor completion randomized low-rank tensor approximation nonconvex regularizers ADMM algorithm 

摘      要：Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD based low-rank approximation, which suffers from high computational costs when dealing with large-scale tensor data. Moreover, most of them are only applicable to third-order tensors. Against these issues, in this article, two efficient low-rank tensor approximation approaches fusing random projection techniques are first devised under the order-d ( d = 3 ) T-SVD framework. Theoretical results on error bounds for the proposed randomized algorithms are provided. On this basis, we then further investigate the robust high-order tensor completion problem, in which a double nonconvex model along with its corresponding fast optimization algorithms with convergence guarantees are developed. Experimental results on large-scale synthetic and real tensor data illustrate that the proposed method outperforms other state-of-the-art approaches in terms of both computational efficiency and estimated precision.