Reparameterized Tensor Ring Functional Decomposition for Multi-Dimensional Data Recovery

Researchers propose a reparameterized Tensor Ring functional decomposition method that uses Implicit Neural Representations to improve multi-dimensional data recovery tasks. The approach addresses limitations in high-frequency modeling through structured reparameterization and demonstrates superior performance in image processing and point cloud recovery applications.

• →New TR functional decomposition extends tensor ring methods to both meshgrid and non-meshgrid data using neural representations.
• →Frequency-domain analysis reveals spectral structure limitations that restrict high-frequency modeling capacity in existing methods.
• →Reparameterized approach combines learnable latent tensors with fixed basis to improve training dynamics.
• →Method shows superior performance across image inpainting, denoising, super-resolution, and point cloud recovery tasks.
• →Research includes theoretical proofs of Lipschitz continuity and principled initialization schemes.