基于截断核范数的张量去噪

doi:10.12677/AAM.2019.810186

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基于截断核范数的张量去噪
Tensor Denoising Based on Truncated Nuclear Norm

DOI: 10.12677/AAM.2019.810186, PDF,
作者: 冯晓亭, 马婷婷：辽宁师范大学数学学院，辽宁大连
关键词: 截断核范数；增广拉格朗日乘子法；张量奇异值分解；图像去噪；Truncated Nuclear Norm； Augmented Lagrange Multipliers； Tensor Singular Value Decomposition； Image Denoising

摘要: 基于张量核范数问题，用截断核范数代替核范数，建立一个新的截断核范数鲁棒主成分分析(Truncated Nuclear Norm Robust Principal Component Analysis, TNNRPCA)模型，并使用增广拉格朗日乘子法对这个凸优化问题求解。在图像去噪的实验过程中，截断核范数的鲁棒主成分分析模型去噪效果好。

Abstract: Based on the problem of tensor nuclear norm, a new robust principal component analysis model is established by substituting truncated nuclear norm for nuclear norm, and the convex optimization problem is solved by augmented Lagrange multiplier method. In the experiment of image denoising, the robust principal component analysis model with truncated unclear norm has good denosing effect.

文章引用：冯晓亭, 马婷婷. 基于截断核范数的张量去噪[J]. 应用数学进展, 2019, 8(10): 1592-1596. https://doi.org/10.12677/AAM.2019.810186

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