重新参数化张量环功能分解用于多维数据恢复
Reparameterized Tensor Ring Functional Decomposition for Multi-Dimensional Data Recovery
AI总结：
本文提出了一种重新参数化的张量环功能分解方法，通过结合可学习的潜在张量和固定基底，提升多维数据恢复的性能。
摘要：
张量环（TR）分解是一种强大的高阶数据建模工具，但本质上受限于离散形式，定义在固定的网格上。在本工作中，我们提出了一种适用于网格和非网格数据的TR功能分解，其中因子由隐式神经表示（INRs）参数化。然而，优化这种连续框架以捕捉细粒度细节本质上是困难的。通过频域分析，我们证明TR因子的谱结构决定了重建张量的频率组成，并限制了高频建模能力。为缓解这一问题，我们提出了一种重新参数化的TR功能分解，其中每个TR因子是可学习的潜在张量和固定基底的结构组合。这种重新参数化在理论上被证明可以改善TR因子学习的训练动态。我们进一步推导了固定基底的原理化初始化方案，并证明了我们所提模型的Lipschitz连续性。在图像修复、去噪、超分辨率和点云恢复的大量实验中，我们的方法在一致性上优于现有方法。代码可在https://github.com/YangyangXu2002/RepTRFD上获得。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
