基于lp正则化双层Tucker秩的张量去噪算法研究
Tensor Denoising Algorithm Based on lp Regularized Two-Layer Tucker Rank
DOI: 10.12677/aam.2026.155246, PDF,   
作者: 姜 萱：太原师范学院数学与统计学院，山西 晋中；付亚茹*：太原师范学院数学与统计学院，山西 晋中；太原师范学院山西省智能优化计算与区块链技术重点实验室，山西 晋中
关键词: 张量去噪；奇异值分解；Tucker秩；ADMM；Tensor Denoising； Singular Value Decomposition； Tucker Rank； ADMM
摘要: 本文研究一种基于lp正则化与双层Tucker秩的张量去噪模型的高效求解算法。在一定参数条件下，模型可通过模态奇异值分解实现对张量低秩结构的精准刻画。本文重点聚焦模型的算法设计与数值实验验证，采用交替方向乘子法(ADMM)构建算法。在随机张量、带噪彩色图像以及结构性缺失彩色图像补全任务上的数值实验结果表明，本文所提方法与其他方法相比，具有更高的补全精度、更清晰的视觉恢复效果，验证了该模型在张量补全任务中的有效性与实用性。
Abstract: This paper investigates an efficient algorithm for a tensor denoising model based on lp regularization and the two-layer Tucker rank. Under some certain parameter conditions, the model can accurately characterize the low-rank structure of tensors via modal singular value decomposition. This work focuses on algorithm design and numerical experimental validation, constructing a algorithm using the Alternating Direction Method of Multipliers (ADMM). Numerical experiments on random tensors, noisy color images, and structurally missing color image completion tasks demonstrate that the proposed method achieves higher completion accuracy, clearer visual recovery results compared with other methods, verifying the effectiveness and practicality of the model in tensor completion tasks.
文章引用：姜萱, 付亚茹. 基于lp正则化双层Tucker秩的张量去噪算法研究[J]. 应用数学进展, 2026, 15(5): 500-510. https://doi.org/10.12677/aam.2026.155246

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