Low-rank tensor completion via combined Tucker and Tensor Train for color image recovery

In recent years, low-rank tensor completion has been widely used in color image recovery. Tensor Train (TT), as a balanced tensor rank minimization method, has achieved good results in actual image recovery because of its ability to capture the hidden information of images. When processing the third-order tensor data of a color image, TT transforms it into a higher-order tensor through kat augmentation to exploit the local feature of the tensor effectively. However, this method actually destroys the original structure of the tensor, which leads to insufficient access to the global structure information. Therefore, the algorithm performs poorly when processing images with a significant amount of missing information. Aiming at this problem, a new tensor completion model is proposed, which combines Tucker rank and Tensor Train rank. Among them, Tucker is used to obtain the global structure information, and Tensor Train is used to capture the local hidden information. To tackle the proposed model, we develop an efficient alternating direction method based algorithm. The numerical experiments using various tensor data show the effectiveness of the model.