  As a new color image representation tool, quaternion has achieved excellent
results in the color image processing, because it treats the color image as a
whole rather than as a separate color space component, thus it can make full
use of the high correlation among RGB channels. Recently, low-rank quaternion
matrix completion (LRQMC) methods have proven very useful for color image
inpainting. In this paper, we propose three novel LRQMC methods based on three
quaternion-based bilinear factor (QBF) matrix norm minimization models.
Specifically, we define quaternion double Frobenius norm (Q-DFN), quaternion
double nuclear norm (Q-DNN) and quaternion Frobenius/nuclear norm (Q-FNN), and
then show their relationship with quaternion-based matrix Schatten-p (Q-
Schatten-p ) norm for certain p values. The proposed methods can avoid
computing quaternion singular value decompositions (QSVD) for large quaternion
matrices, and thus can effectively reduce the calculation time compared with
existing (LRQMC) methods. The experimental results demonstrate the superior
performance of the proposed methods over some state-of-the-art low-rank
(quaternion) matrix completion methods.
