  Tensor completion is a challenging problem with various applications. Many
related models based on the low-rank prior of the tensor have been proposed.
However, the low-rank prior may not be enough to recover the original tensor
from the observed incomplete tensor. In this paper, we prose a tensor
completion method by exploiting both the low-rank and sparse prior of tensor.
Specifically, the tensor completion task can be formulated as a low-rank
minimization problem with a sparse regularizer. The low-rank property is
depicted by the tensor truncated nuclear norm based on tensor singular value
decomposition (T-SVD) which is a better approximation of tensor tubal rank than
tensor nuclear norm. While the sparse regularizer is imposed by a
$\ell_{1}$-norm in a discrete cosine transformation (DCT) domain, which can
better employ the local sparse property of completed data. To solve the
optimization problem, we employ an alternating direction method of multipliers
(ADMM) in which we only need to solve several subproblems which have
closed-form solutions. Substantial experiments on real world images and videos
show that the proposed method has better performances than the existing
state-of-the-art methods.
