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<p>This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional with two regularization terms: one promotes low-rank structure in the solution, while the other one enforces smoothness. To solve the resulting optimization problem, we employ the alternating direction method of multipliers (ADMM). A detailed convergence analysis of the algorithm is provided and the performance of the methods is demonstrated through a series of numerical experiments.</p>

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Low-rank Regularized convex-non-convex problems for image segmentation and completion

  • 期刊论文

  • 发表日期：

    2026年5月5日

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  • M. El Guide,
  • A. El Hachimi,
  • K. Jbilou,
  • L. Reichel

摘要

This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional with two regularization terms: one promotes low-rank structure in the solution, while the other one enforces smoothness. To solve the resulting optimization problem, we employ the alternating direction method of multipliers (ADMM). A detailed convergence analysis of the algorithm is provided and the performance of the methods is demonstrated through a series of numerical experiments.