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<p>In this paper, we consider a system of monotonic inclusions involving three operators in real Hilbert spaces with the third being linearly composed. Such problems frequently arise in fields such as image processing, clustering, and others. We propose a new splitting algorithm to address this issue, extending the unknown variables to matrix form. A key advantage of our algorithm is that at each iteration, it requires computing only the resolvent of each individual operator, which can be evaluated independently and thus is amenable to parallel computation. Weak convergence is established using the eigenoperator technique. Numerical experiments demonstrate that the proposed algorithm significantly outperforms some representative state-of-the-art methods in image testing problems and achieves competitive performance in nonnegative matrix factorization (NMF)-based clustering tasks compared to some other algorithms.</p>

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A practical three-operator splitting method with applications to image and clustering problems

  • 期刊论文

  • 发表日期：

    2026年3月12日

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  • Wenya Shi,
  • Yunda Dong,
  • Zhixiang Chen

摘要

In this paper, we consider a system of monotonic inclusions involving three operators in real Hilbert spaces with the third being linearly composed. Such problems frequently arise in fields such as image processing, clustering, and others. We propose a new splitting algorithm to address this issue, extending the unknown variables to matrix form. A key advantage of our algorithm is that at each iteration, it requires computing only the resolvent of each individual operator, which can be evaluated independently and thus is amenable to parallel computation. Weak convergence is established using the eigenoperator technique. Numerical experiments demonstrate that the proposed algorithm significantly outperforms some representative state-of-the-art methods in image testing problems and achieves competitive performance in nonnegative matrix factorization (NMF)-based clustering tasks compared to some other algorithms.