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基于非凸优化模型张量补全的RIP条件

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限制等距条件在稀疏优化中具有重要的意义,它是稀疏性的保证.在压缩感知和矩阵补全中,基于l1,L*以及l1-l2和L*-LF优化模型的限制等距条件已经获得较丰富的成果.本文将推广到张量上,基于Tucker秩和L*-LF优化模型,研究低秩张量x恢复的限制等距性质(RIP),给出限制等距性常数δ2rn的一个界.
RIP Conditions Based on Non-convex Optimization Model for Tensor Completion
The restricted isometric condition is of great importance in sparse optimization as a guarantee of sparsity.Many results have been obtained in compressed perception and matrix completion based on l1,L*,l1-l2 and L*-LF optimization models with restricted isometric conditions.In this paper,we extend them to tensors,and study the restricted isometry property(RIP)recovered from low-rank tensors X and give a bound on the constant δ2rn,based on the Tucker rank and L*-LF optimization models.

‖x‖*-‖x‖F minimizationRestricted isometry propertyLow-rank tensor recovery

王川龙、钟林江

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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 030619

‖x‖*-‖x‖F最小化 限制等距性 低秩张量恢复

2025

应用数学
华中科技大学

应用数学

北大核心
影响因子:0.234
ISSN:1001-9847
年,卷(期):2025.38(1)