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<p>In this paper, we propose an over-relaxed forward–backward–forward splitting algorithm incorporating a momentum technique to solve a monotone inclusion problem in a real Hilbert space. We establish both weak and linear convergence results for the proposed algorithm under standard assumptions. Notably, some existing forward–backward–forward splitting algorithms are recovered as special cases of our algorithm. Numerical experiments on variational inequality problems and real-world applications in signal recovery and image restoration demonstrate that our algorithm outperforms existing forward–backward–forward splitting algorithms.</p>

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A New Numerically Fast Relaxed Forward–Backward–Forward Algorithm with Applications to Compressed Sensing and Image Processing

  • 期刊论文

  • 发表日期：

    2025年9月4日

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  • Yong-Hong Yao,
  • Ren-Qi Xu,
  • Abubakar Adamu,
  • Yekini Shehu

摘要

In this paper, we propose an over-relaxed forward–backward–forward splitting algorithm incorporating a momentum technique to solve a monotone inclusion problem in a real Hilbert space. We establish both weak and linear convergence results for the proposed algorithm under standard assumptions. Notably, some existing forward–backward–forward splitting algorithms are recovered as special cases of our algorithm. Numerical experiments on variational inequality problems and real-world applications in signal recovery and image restoration demonstrate that our algorithm outperforms existing forward–backward–forward splitting algorithms.