  The use of quaternions as a novel tool for color image representation has
yielded impressive results in color image processing. By considering the color
image as a unified entity rather than separate color space components,
quaternions can effectively exploit the strong correlation among the RGB
channels, leading to enhanced performance. Especially, color image inpainting
tasks are highly beneficial from the application of quaternion matrix
completion techniques, in recent years. However, existing quaternion matrix
completion methods suffer from two major drawbacks. First, it can be difficult
to choose a regularizer that captures the common characteristics of natural
images, and sometimes the regularizer that is chosen based on empirical
evidence may not be the optimal or efficient option. Second, the optimization
process of quaternion matrix completion models is quite challenging because of
the non-commutativity of quaternion multiplication. To address the two
drawbacks of the existing quaternion matrix completion approaches mentioned
above, this paper tends to use an untrained quaternion convolutional neural
network (QCNN) to directly generate the completed quaternion matrix. This
approach replaces the explicit regularization term in the quaternion matrix
completion model with an implicit prior that is learned by the QCNN. Extensive
quantitative and qualitative evaluations demonstrate the superiority of the
proposed method for color image inpainting compared with some existing
quaternion-based and tensor-based methods.
