改进的低秩张量逼近算法
Enhanced Low Rank Tensor Approximation Algorithm
摘要: 本文在低秩矩阵逼近(Low-rank Matrix Approximation, LRMA)问题的基础上将其推广到张量上，提出了利用非凸正则化构造凸优化问题来估计低秩张量的方法，采用参数化的非凸罚函数估计非零的奇异值，并求出了该目标函数的全局最优解。实验结果表明，该方法能很好处理低秩张量逼近问题，实现图像去噪。
Abstract: In this paper, we extended the low rank matrix approximation problem to tensors. A method for estimating low-rank tensors by constructing convex optimization problems with non-convex reg-ularization is proposed. The non-zero singular values are estimated by parameterized non-convex penalty functions, and the global optimal solution of the objective function is obtained. The ex-perimental results show that this method can deal with the low rank tensor approximation problem very well and achieve image denoising.
文章引用：马婷婷, 冯晓亭. 改进的低秩张量逼近算法[J]. 应用数学进展, 2019, 8(8): 1336-1340. https://doi.org/10.12677/AAM.2019.88157

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