Reparameterized Tensor Ring Functional Decomposition for Multi-Dimensional Data Recovery

• URL: http://arxiv.org/abs/2603.01034v1
• Date: Sun, 01 Mar 2026 10:19:03 GMT
• Title: Reparameterized Tensor Ring Functional Decomposition for Multi-Dimensional Data Recovery
• Authors: Yangyang Xu, Junbo Ke, You-Wei Wen, Chao Wang,
• Abstract summary: Ring (TR) decomposition is a powerful tool for high-order data modeling.<n>We propose a TR functional decomposition for both meshgrid and non-meshgrid data.<n>We show that the spectral structure of TR factors determines the frequency composition of the reconstructed tensor.
• Score: 14.632447227551864
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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