  A novel low-rank completion algorithm based on the quaternion tensor is
proposed in this paper. This approach uses the TQt-rank of quaternion tensor to
maintain the structure of RGB channels throughout the entire process. In more
detail, the pixels in each frame are encoded on three imaginary parts of a
quaternion as an element in a quaternion matrix. Each quaternion matrix is then
stacked into a quaternion tensor. A logarithmic function and truncated nuclear
norm are employed to characterize the rank of the quaternion tensor in order to
promote the low rankness of the tensor. Moreover, by introducing a newly
defined quaternion tensor discrete cosine transform-based (QTDCT)
regularization to the low-rank approximation framework, the optimized recovery
results can be obtained in the local details of color videos. In particular,
the sparsity of the quaternion tensor is reasonably characterized by l1 norm in
the QDCT domain. This strategy is optimized via the two-step alternating
direction method of multipliers (ADMM) framework. Numerical experimental
results for recovering color videos show the obvious advantage of the proposed
method over other potential competing approaches.
