  The T-product method based upon Discrete Fourier Transformation (DFT) has
found wide applications in engineering, in particular, in image processing. In
this paper, we propose variable T-product, and apply the Zero-Padding Discrete
Fourier Transformation (ZDFT), to convert third order tensor problems to the
variable Fourier domain. An additional positive integer parameter is
introduced, which is greater than the tubal dimension of the third order
tensor. When the additional parameter is equal to the tubal dimension, the ZDFT
reduces to DFT. Then, we propose a new tensor completion method based on ZDFT
and TV regularization, called VTCTF-TV. Extensive numerical experiment results
on visual data demonstrate that the superior performance of the proposed
method. In addition, the zero-padding is near the size of the original tubal
dimension, the resulting tensor completion can be performed much better.
