Quaternion Matrix Completion

Quaternion matrix completion focuses on recovering missing data in color images and videos by representing them as quaternion matrices, leveraging the inherent coupling between color channels. Current research emphasizes developing robust low-rank quaternion matrix completion models, often incorporating techniques like sparse regularization, tensor decompositions (e.g., tensor ring), and iterative reweighted minimization algorithms to improve accuracy and efficiency. These advancements are significant for applications in image and video inpainting, where they offer improved performance over traditional methods by effectively handling the multi-channel nature of color data.