Quaternion matrix completion (QMC) aims to accurately recover multi-channel data exhibiting inter channel dependencies from incomplete observations. However, in the scenarios with large singular value disparities, traditional nuclear norm-based methods often fail to capture the true low-rank struc ture, which results in recovery deviation. Meanwhile, the non-commutativity and structural complexity of quaternion algebra pose significant challenges for quaternion low-rank modeling and optimization. Despite their empirically promising performance, existing QMC methods generally provide conver gence analysis but lack the bound of the convergence. To address these challenges, we propose a novel quaternion completion method based on a smooth log-determinant surrogate with a dynamic parameter termed QCSLD,whicheffectively captures the low-rank structure of hypercomplex multi-channel data even under severe singular value disparities. To ensure numerical stability and theoretical convergence, wedevelop an efficient iterative algorithm and provide an explicit quadratic bound on the convergence behavior under mild assumptions, which ensures predictability and stability for QMC. Experiments on synthetic and real datasets further validate that QCSLD achieves superior reconstruction accuracy compared to generally comparison method.
Xiao et al. (Mon,) studied this question.