用神经网络重构张量，让图像点云恢复更精准。
Reparameterized Tensor Ring Functional Decomposition for Multi-Dimensional Data Recovery
- 用隐式神经表示重参数化张量环分解，支持网格与非网格数据。
- 在图像修复、去噪、超分和点云恢复上均超越现有方法。
- 理论证明模型连续性并设计了有效初始化方案，训练更稳定。
张量环（TR）分解是高阶数据建模的强大工具，但其固有局限在于仅适用于固定网格上的离散形式。本文提出一种基于隐式神经表示（INRs）的连续型TR功能分解方法，可处理网格与非网格数据。然而，优化该连续框架以捕捉精细细节存在内在困难。通过频域分析，我们发现TR因子的谱结构决定了重构张量的频率组成，并限制了高频建模能力。为此，提出重参数化TR功能分解，其中每个因子由可学习的潜在张量与固定基函数组合而成。该重参数化被理论证明能改善因子学习的训练动态。进一步推导出固定基的合理初始化方案，并证明了所提模型的Lipschitz连续性。在图像修补、去噪、超分辨率及点云恢复上的大量实验表明，该方法性能持续优于现有方法。代码已开源：https://github.com/YangyangXu2002/RepTRFD。
原文摘要 · Abstract (English)
Tensor Ring (TR) decomposition is a powerful tool for high-order data modeling, but is inherently restricted to discrete forms defined on fixed meshgrids. In this work, we propose a TR functional decomposition for both meshgrid and non-meshgrid data, where factors are parameterized by Implicit Neural Representations (INRs). However, optimizing this continuous framework to capture fine-scale details is intrinsically difficult. Through a frequency-domain analysis, we demonstrate that the spectral structure of TR factors determines the frequency composition of the reconstructed tensor and limits the high-frequency modeling capacity. To mitigate this, we propose a reparameterized TR functional decomposition, in which each TR factor is a structured combination of a learnable latent tensor and a fixed basis. This reparameterization is theoretically shown to improve the training dynamics of TR factor learning. We further derive a principled initialization scheme for the fixed basis and prove the Lipschitz continuity of our proposed model. Extensive experiments on image inpainting, denoising, super-resolution, and point cloud recovery demonstrate that our method achieves consistently superior performance over existing approaches. Code is available at https://github.com/YangyangXu2002/RepTRFD.
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