Robust Tensor SVD and Recovery With Rank Estimation.

Area of Science:

• Multidimensional Data Analysis
• Numerical Linear Algebra

Background:

• Tensor singular value decomposition (t-SVD) is widely used for tensor recovery.
• Existing t-SVD methods lack accurate rank estimation, limiting recovery performance.
• Tensor rank estimation is a challenging problem.

Purpose of the Study:

• To develop accurate rank estimation for low-rank tensors from corrupted observations using t-SVD.
• To improve tensor recovery performance by utilizing the estimated rank.
• To propose robust methods for tensor completion and principal component analysis with rank estimation.

Main Methods:

• Establishing an equivalence between tensor nuclear norm (TNN) and the f-diagonal tensor.
• Simultaneously minimizing reconstruction error and TNN for rank estimation.
• Developing robust tensor principal component analysis and tensor completion models incorporating rank estimation.

Main Results:

• The proposed methods achieve accurate rank estimation for intrinsic low-rank tensors.
• Relaxing the TNN regularizer enhances tensor recovery performance.
• Robust methods demonstrate successful recovery from missing data and gross corruptions.
• Experimental results show significant improvements over state-of-the-art methods.

Conclusions:

• Accurate rank estimation is crucial for enhancing t-SVD-based tensor recovery.
• The proposed robust methods offer superior performance in tensor completion and principal component analysis.
• This work provides a significant advancement in handling corrupted and incomplete tensor data.