  In the present paper we propose two new algorithms of tensor completion for
three-order tensors. The proposed methods consist in minimizing the average
rank of the underlying tensor using its approximate function namely the tensor
nuclear norm and then the recovered data will be obtained by using the total
variation regularisation technique. We will adopt the Alternating Direction
Method of Multipliers (ADM), using the tensor T-product, to solve the main
optimization problems associated to the two algorithms. In the last section, we
present some numerical experiments and comparisons with the most known image
completion methods.
