Stable Tensor Principal Component Pursuit: Error Bounds and Efficient Algorithms

Area of Science:

• Multi-dimensional data analysis
• Signal processing
• Machine learning

Background:

• Sensor technology generates vast amounts of multi-dimensional array (tensor) data.
• Tensor data is susceptible to noise and gross corruptions from sensor failures or data loss.

Purpose of the Study:

• To develop a robust method for recovering corrupted tensor data.
• To introduce a Stable Tensor Principal Component Pursuit (STPCP) model utilizing the tubal nuclear norm (TNN).

Main Methods:

• Proposed a STPCP model based on the tubal nuclear norm (TNN).
• Developed an Alternating Direction Method of Multipliers (ADMM) algorithm.
• Designed an accelerated algorithm using orthogonal tensor factorization.

Main Results:

• Theoretically proved stable recovery of underlying and corruption tensors under incoherence conditions.
• Demonstrated superior performance and efficiency compared to other tensor nuclear norms.
• Validated the proposed algorithms on synthetic and real-world datasets.

Conclusions:

• The proposed STPCP model and algorithms effectively recover corrupted tensor data.
• The tubal nuclear norm offers advantages over existing tensor norms for robust recovery.
• The developed methods show practical applicability in handling real-world corrupted tensor data.