改进的鲁棒低秩正则化张量填充
Improved Robust Low-Rank Regularization Tensor Completion
DOI: 10.12677/AAM.2022.1111809, PDF,    科研立项经费支持
作者: 王香懿：辽宁师范大学，辽宁 大连；姜 伟：辽宁师范大学，辽宁 大连；温州大学，浙江 温州
关键词: 张量填充；加权张量核范数；加权张量Frobenius范数；Tensor Completion； Weighted Tensor Nuclear Norm； Weighted Tensor Frobenius Norm
摘要: 考虑到传统张量核范数作为秩函数的凸松弛在实际优化效果上的不足，本文借助非凸松弛的思想，提出了由加权张量核范数和加权张量Frobenius范数组合而成的新的非凸的张量填充模型，并运用交替方向乘子法求解所提出的低秩张量恢复模型。在张量填充方面，该模型在PSNR指标和视觉感知方面均优于传统方法，也取得了比传统算法更好的性能。
Abstract: Considering the deficiency of the convex relaxation of the traditional tensor nuclear norm as a rank function in the actual optimization effect, this paper proposes a new non convex tensor completion model composed of weighted tensor nuclear norm and weighted tensor Frobenius norm by virtue of the idea of non convex relaxation, and uses the alternating direction multiplier method to solve the proposed low rank tensor recovery model. In terms of tensor filling, the model is superior to the traditional methods in terms of PSNR index and visual perception, and has achieved better perfor-mance than the traditional algorithm.
文章引用：王香懿, 姜伟. 改进的鲁棒低秩正则化张量填充[J]. 应用数学进展, 2022, 11(11): 7647-7652. https://doi.org/10.12677/AAM.2022.1111809

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