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<p>As an innovative method for color image completion, low-rank quaternion matrix completion (LRQMC) treats color images as unified quaternion structures, effectively capturing the high correlations among RGB channels. With the integration of the low-rank prior for matrices, LRQMC demonstrates excellent performance in image completion tasks. Building upon this, this paper proposes a quaternion matrix factorization method based on continuous functions, where the original quaternion matrix is represented as the product of two smaller factor matrices constructed via continuous functions. Furthermore, it is theoretically proven that this factorization method inherently possesses a low-rank constraint, and explicit regularization priors are introduced to promote smoother image recovery. Numerical experiments demonstrate that the proposed method not only offers superior computational efficiency but also significantly outperforms traditional LRQMC methods in terms of image quality and quantitative evaluation metrics.</p>

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Quaternion matrix function representation for color image recovery

  • 期刊论文

  • 发表日期：

    2025年10月9日

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  • Jinping Zou,
  • Huan Ren,
  • Xiang Wang

摘要

As an innovative method for color image completion, low-rank quaternion matrix completion (LRQMC) treats color images as unified quaternion structures, effectively capturing the high correlations among RGB channels. With the integration of the low-rank prior for matrices, LRQMC demonstrates excellent performance in image completion tasks. Building upon this, this paper proposes a quaternion matrix factorization method based on continuous functions, where the original quaternion matrix is represented as the product of two smaller factor matrices constructed via continuous functions. Furthermore, it is theoretically proven that this factorization method inherently possesses a low-rank constraint, and explicit regularization priors are introduced to promote smoother image recovery. Numerical experiments demonstrate that the proposed method not only offers superior computational efficiency but also significantly outperforms traditional LRQMC methods in terms of image quality and quantitative evaluation metrics.