Reproduce “Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery” on OpenResearch

About this paper

Yisi Luo, Xile Zhao, Zhemin Li, Michael K. Ng, Deyu Meng

This work introduces Low-Rank Tensor Function Representation (LRTFR), a novel framework for continuously representing multi-dimensional data by extending discrete low-rank tensor models to the function domain. It demonstrates superior performance in tasks like multi-dimensional image inpainting, multispectral image denoising, hyperparameter optimization, and point cloud upsampling, particularly excelling in scenarios requiring inference beyond original discrete data points.

Key insights

• The paper establishes a theoretical framework that unifies discrete low-rank tensor analysis with continuous data representation through the introduction of 'tensor function' and 'Function Rank (F-rank)'.
• The proposed Low-Rank Tensor Function Representation (LRTFR) implicitly encodes both low-rankness and Lipschitz smoothness, alleviating the need for explicit regularization and enhancing stability compared to generic Implicit Neural Representations (INRs).
• Parameterizing the factor functions with Multi-Layer Perceptrons (MLPs) allows for powerful approximation of continuous multi-dimensional data while significantly reducing the computational burden and overfitting issues common in standard INRs.

Summary by alphaXiv.