#4282. Weighted truncated nuclear norm regularization for low-rank quaternion matrix completion

September 2026publication date
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Journal’s subject area:
Visual Arts and Performing Arts;
Communication;
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Abstract:
In recent years, quaternion matrix completion (QMC) based on low-rank regularization has been gradually used in image processing. Unlike low-rank matrix completion (LRMC) which handles RGB images by recovering each color channel separately, QMC models retain the connection of three channels and process them as a whole. Most of the existing quaternion-based methods formulate low-rank QMC (LRQMC) as a quaternion nuclear norm (a convex relaxation of the rank) minimization problem. To achieve a more accurate low-rank approximation, we introduce a quaternion truncated nuclear norm (QTNN) for LRQMC and utilize the alternating direction method of multipliers (ADMM) to get the optimization in this paper. The weighted method utilizes a concise gradient descent strategy which has a theoretical guarantee in optimization. The effectiveness of our method is illustrated by experiments on real visual data sets.
Keywords:
Low-rank; Quaternion matrix completion; Quaternion truncated nuclear norm; Weights

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