Quaternion matrix completion with total variation regularization utilizing fast dual proximal gradient method

Quaternion matrix completion, which aims to recover original images from incomplete data, has recently gained significant attention in the fields of image and signal processing. Unlike traditional models that only consider the low-rankness of the recovered image, we propose a novel model that combines the Geman function and anisotropic or isotropic total variation (TV) regularization. In the process of solving the model using the Alternating Direction Method of Multipliers (ADMM) algorithm, we also employ the Fast Dual Proximal Gradient Method to address the corresponding sub-problem related to the TV regularization. The numerical results on color images demonstrate the effectiveness and reliability of the proposed algorithm.