Low Rank Tensor Completion With Poisson Observations

Area of Science:

• Computer Vision
• Signal Processing
• Machine Learning

Background:

• Poisson observations are key for modeling video data in computer vision.
• Tensor completion aims to reconstruct tensors from limited observed entries.
• Existing matrix-based methods for tensor completion can be suboptimal for video data.

Purpose of the Study:

• To address the challenge of third-order tensor completion with Poisson observations.
• To develop a more effective tensor completion method that leverages global low-rank properties.
• To improve the accuracy of recovering underlying tensors from sparse Poisson-sampled video data.

Main Methods:

• Utilizing maximum likelihood estimation for Poisson distributions.
• Employing Kullback-Leibler divergence for data-fitting.
• Introducing a transformed tensor nuclear norm ball constraint with bounded entry constraints.
• Developing an alternating direction method of multipliers (ADMM) for optimization.

Main Results:

• The proposed model demonstrates a lower error bound compared to existing matrix-based methods.
• An information-theoretic lower error bound for the problem is established.
• Numerical experiments validate the model's effectiveness on synthetic and real-world datasets.

Conclusions:

• The proposed tensor completion method offers superior performance for Poisson observations in video processing.
• The novel approach effectively utilizes tensor properties for more accurate reconstruction.
• The developed optimization technique provides an efficient solution for the convex problem.