Robust Low-Rank Tensor Recovery With Regularized Redescending M-Estimator

Area of Science:

• Mathematics
• Computer Science
• Statistics

Background:

• Tensor recovery reconstructs low-rank tensors from linear measurements, crucial for image processing and machine learning.
• Real-world data often contains sparse outliers, challenging existing tensor recovery methods.
• Current approaches lack robustness against significant data contamination.

Purpose of the Study:

• To develop robust low-rank tensor recovery methods resilient to sparse gross errors.
• To introduce novel algorithms addressing computational challenges posed by non-convexity in robust estimation.
• To ensure the effectiveness and convergence of proposed methods in outlier-prone scenarios.

Main Methods:

• Utilizing regularized redescending M-estimators from robust statistics for outlier handling.
• Developing proximal and linearized block coordinate descent algorithms for computational efficiency.
• Analyzing algorithm convergence using the Kurdyka-Łojasiewicz property and Lipschitz continuity.

Main Results:

• Proposed methods demonstrate significant robustness in the presence of outliers.
• Algorithms maintain effectiveness even when data is not contaminated.
• Numerical experiments confirm the practical performance on synthetic and real datasets.
• The developed algorithms exhibit guaranteed descent properties and global convergence.

Conclusions:

• The proposed regularized redescending M-estimators offer a robust solution for low-rank tensor recovery.
• The novel algorithms effectively overcome computational difficulties associated with non-convexity.
• These methods provide a reliable tool for applications dealing with potentially corrupted tensor data.