Robust Low-Rank Tensor Recovery with Rectification and Alignment.

Area of Science:

• Data Science
• Applied Mathematics
• Computer Vision

Background:

• Low-rank tensor recovery is crucial for analyzing complex datasets.
• Existing methods struggle with sparse errors and data deformation.
• Simultaneous rectification and alignment are needed for robust recovery.

Purpose of the Study:

• To propose a general framework for low-rank tensor recovery.
• To address data deformation and sparse errors concurrently.
• To provide a unified approach encompassing existing methods.

Main Methods:

• Developed surrogate-based formulations for unified rectification and alignment.
• Derived optimization algorithms using ADMM and proximal gradient methods.
• Established worst-case error bounds for tensor recovery.

Main Results:

• The proposed framework integrates rectification and alignment, surpassing individual methods like RASL and TILT.
• Two novel algorithms (ADMM-based and proximal gradient) were developed for optimization.
• Convergence guarantees were proven for the proximal gradient algorithm.

Conclusions:

• The proposed framework offers a comprehensive solution for low-rank tensor recovery with sparse errors and transformations.
• The developed algorithms demonstrate effectiveness and efficiency on public datasets.
• This work advances the field by unifying and extending existing tensor recovery techniques.