Low-Tubal-Rank Plus Sparse Tensor Recovery With Prior Subspace Information

Area of Science:

• Multidimensional data analysis
• Tensor decomposition
• Machine learning

Background:

• Tensor Principal Component Pursuit (TPCP) is a key method in Tensor Robust Principal Component Analysis (TRPCA).
• Standard TPCP relies on strict tensor incoherence conditions, limiting its practical application.
• Robust decomposition of data tensors into low-tubal-rank and sparse components is crucial in many fields.

Purpose of the Study:

• To develop an improved TPCP method that relaxes restrictive incoherence assumptions.
• To leverage prior subspace information for more robust tensor decomposition.
• To provide an efficient algorithm for the proposed method.

Main Methods:

• Proposed Modified-TPCP by integrating prior subspace information into the TRPCA framework.
• Developed an efficient algorithm using the Alternating Direction Method of Multipliers (ADMM) for Modified-TPCP.
• Evaluated the method through simulations and real-world data applications.

Main Results:

• Modified-TPCP successfully recovers low-tubal-rank and sparse components under significantly weaker incoherence conditions.
• The ADMM-based algorithm provides efficient implementation of the proposed method.
• Simulations and real data demonstrated the effectiveness and robustness of Modified-TPCP.

Conclusions:

• Modified-TPCP offers a more practical and robust approach to tensor decomposition compared to standard TPCP.
• Incorporating prior subspace information is a valuable strategy for enhancing TRPCA methods.
• The proposed ADMM algorithm ensures efficient and effective application of Modified-TPCP.