A tensor completion method based on tensor QR decomposition with truncated nuclear norm and sparse regularization

Tensor completion is an important problem in machine learning and signal processing. While the completion method based on tensor singular value decomposition has good accuracy, it can be computationally expensive when dealing with large datasets. To improve the calculation speed, we propose a truncated nuclear norm based on tensor QR decomposition and sparse regularization tensor completion algorithm (TQR-TNNSR) in this paper. This method combines the sparse regularization term of SRTD and uses three-factor tensor decomposition to calculate only a small tensor truncation nuclear norm minimization problem, significantly reducing computational cost. Our experiments on color images, videos, and MRI data show that TQR-TNNSR has low computational cost and high recovery speed while maintaining high recovery accuracy. The advantages of recovery accuracy and speed are more pronounced in higher-dimensional scenarios.