  Low-rank quaternion tensor completion method, a novel approach to recovery
color videos and images is proposed in this paper. We respectively reconstruct
a color image and a color video as a quaternion matrix (second-order tensor)
and a third-order quaternion tensor by encoding the red, green, and blue
channel pixel values on the three imaginary parts of a quaternion. Different
from some traditional models which treat color pixel as a scalar and represent
color channels separately, whereas, during the quaternion-based reconstruction,
it is significant that the inherent color structures of color images and color
videos can be completely preserved. Under the definition of Tucker rank, the
global low-rank prior to quaternion tensor is encoded as the nuclear norm of
unfolding quaternion matrices. Then, by applying the ADMM framework, we provide
the tensor completion algorithm for any order quaternion tensors, which
theoretically can be well used to recover missing entries of any
multidimensional data with color structures. Simulation results for color
videos and color images recovery show the superior performance and efficiency
of the proposed method over some state-of-the-art existing ones.
