Tensor completion for estimating missing values in visual data.

Area of Science:

• Computer Vision
• Machine Learning
• Data Science

Background:

• Missing data in visual tensors is common due to acquisition errors or outlier removal.
• Existing matrix completion techniques using trace norms are effective but not directly applicable to higher-order tensors.
• There is a need for robust tensor completion methods that can handle complex, multi-dimensional data.

Purpose of the Study:

• To propose the first definition of tensor trace norm, generalizing matrix trace norm.
• To develop algorithms for tensor completion based on this new norm.
• To address the computational challenges in solving tensor completion as a convex optimization problem.

Main Methods:

• Definition of tensor trace norm.
• Formulation of tensor completion as a convex optimization problem.
• Development of three algorithms: SiLRTC (simple low rank tensor completion), FaLRTC (fast low rank tensor completion), and HaLRTC (high accuracy low rank tensor completion) using techniques like block coordinate descent, smoothing schemes, and ADMM.

Main Results:

• Proposed algorithms demonstrate accuracy and robustness compared to heuristic approaches.
• SiLRTC offers a simple, globally optimal solution.
• FaLRTC and HaLRTC provide efficient solutions, with FaLRTC excelling for lower accuracy and HaLRTC for higher accuracy.

Conclusions:

• The developed tensor completion algorithms effectively estimate missing values in visual data.
• These methods generalize matrix completion principles to tensors, enabling the filling of larger missing regions.
• The algorithms offer a trade-off between speed and accuracy, catering to different application needs.