Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery.

Area of Science:

• Machine Learning
• Computer Vision
• Data Representation

Background:

• Higher-order tensors are suitable for multi-dimensional data like images and videos.
• Classical low-rank tensor methods are limited to discrete data on meshgrids.
• A need exists for continuous multi-dimensional data representation beyond meshgrids.

Purpose of the Study:

• To propose a novel low-rank tensor function representation (LRTFR) for continuous multi-dimensional data.
• To extend low-rank tensor concepts to functions parameterized by MLPs.
• To demonstrate LRTFR's effectiveness in data recovery tasks.

Main Methods:

• Developed low-rank tensor function representation (LRTFR) using multilayer perceptrons (MLPs).
• Defined tensor function rank and low-rank tensor function factorization for continuous data.
• Utilized MLPs to parameterize factor functions for continuous representation.

Main Results:

• LRTFR unifies low-rank and smooth regularizations for effective and efficient continuous data representation.
• Demonstrated superiority over state-of-the-art methods in multi-dimensional data recovery.
• Validated performance in image inpainting, denoising, hyperparameter optimization, and point cloud upsampling.

Conclusions:

• LRTFR offers a powerful and versatile approach for continuous multi-dimensional data representation.
• The method excels in applications beyond traditional meshgrid limitations.
• LRTFR shows significant potential for advancing machine learning and computer vision tasks.