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<p>This study introduces a new three term hybrid conjugate gradient method for large-scale unconstrained optimization and applies it in image restoration problems. The new conjugate gradient variant is defined by a convex combination of the AlBayati–AlAssady (BA), Fletcher–Reeves (FR), and Polak–Ribière–Polyak (PRP) formulas. The method satisfies the sufficient descent property and its global convergence is established under the strong Wolfe line search. The algorithm is implemented in Python, and its numerical performance is evaluated using Dolan–Moré performance profiles against some classical methods on a collection of well known test functions. As an application, the proposed method is further assessed on image restoration problems in terms of both reconstruction quality and computational efficiency, and is compared with the BA, FR, and PRP algorithms.</p>

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Development of a three term hybrid conjugate gradient method with enhanced convergence for image restoration

  • 期刊论文

  • 发表日期：

    2026年7月17日

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  • Alaa Luqman Ibrahim,
  • Nabil Sellami,
  • Romaissa Mellal

摘要

This study introduces a new three term hybrid conjugate gradient method for large-scale unconstrained optimization and applies it in image restoration problems. The new conjugate gradient variant is defined by a convex combination of the AlBayati–AlAssady (BA), Fletcher–Reeves (FR), and Polak–Ribière–Polyak (PRP) formulas. The method satisfies the sufficient descent property and its global convergence is established under the strong Wolfe line search. The algorithm is implemented in Python, and its numerical performance is evaluated using Dolan–Moré performance profiles against some classical methods on a collection of well known test functions. As an application, the proposed method is further assessed on image restoration problems in terms of both reconstruction quality and computational efficiency, and is compared with the BA, FR, and PRP algorithms.