基于混合截断范数的张量鲁棒主成分分析
Tensor Robust Principal Component Analysis Based on Hybrid Truncation Norm
DOI: 10.12677/AAM.2022.1110783, PDF,    科研立项经费支持
作者: 栾育洁*：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: 张量鲁棒主成分分析；混合截断；交替方向乘子法；Tensor Robust Principal Component Analysis (TRPCA)； Hybrid Truncation Norm； Alternating Direction Multiplier Method (ADMM)
摘要: 本文将截断核范数正则化的思想推广到张量鲁棒主成分分析。为提高模型的稳定性，新定义了张量截断Frobenius范数，并给出同时考虑张量截断核范数和截断Frobenius范数的混合截断模型。这种方法只会最小化min(m,n)-r个奇异值。此外，本文还给出一种确定收缩算子的有效方法，并为此方法开发了一种基于交替方向的有效迭代算法来解决这个优化问题。实验结果表明，该方法可以有效并准确地实现图像去噪。
Abstract: In this paper, the idea of truncated nuclear norm regularization is extended to tensor robust prin-cipal component analysis. In order to improve the stability of the model, the tensor truncated Fro-benius norm is defined, and a mixed truncated model considering both tensor truncated nuclear norm and truncated Frobenius norm is given. This method minimizes min(m,n)-r singular val-ues. In addition, this paper also gives an effective method to determine the contraction operator, and develops an effective iterative algorithm based on alternate directions to solve this optimiza-tion problem. The experimental results show that this method can effectively and accurately realize image denoising.
文章引用：栾育洁, 姜伟. 基于混合截断范数的张量鲁棒主成分分析[J]. 应用数学进展, 2022, 11(10): 7373-7379. https://doi.org/10.12677/AAM.2022.1110783

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