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<p>Ill-posed inverse problems are pervasive across scientific and engineering disciplines, with solutions highly sensitive to data perturbations. Among regularization strategies to mitigate this instability, iterative methods have proven effective. In this paper, we propose an accelerated iterative regularization strategy for solving ill-posed linear operator equations, inspired by nonstationary iterated Tikhonov regularization. The method incorporates a priori and a posteriori parameter selection rules, both of which yield optimal-order error estimates. Compared to existing iterative approaches, the proposed strategy significantly reduces the number of iterations required for convergence under suitable stopping criteria. Numerical experiments validate its efficacy, demonstrating robust performance in solving ill-posed problems. Furthermore, the method’s adaptability is showcased through applications to image restoration, highlighting its practical relevance.</p>

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An accelerated iterative regularization scheme for linear ill-posed problems

  • 期刊论文

  • 发表日期：

    2026年5月18日

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  • Tahar Bechouat,
  • Nadjib Boussetila,
  • Abdelghani Lakhdari

摘要

Ill-posed inverse problems are pervasive across scientific and engineering disciplines, with solutions highly sensitive to data perturbations. Among regularization strategies to mitigate this instability, iterative methods have proven effective. In this paper, we propose an accelerated iterative regularization strategy for solving ill-posed linear operator equations, inspired by nonstationary iterated Tikhonov regularization. The method incorporates a priori and a posteriori parameter selection rules, both of which yield optimal-order error estimates. Compared to existing iterative approaches, the proposed strategy significantly reduces the number of iterations required for convergence under suitable stopping criteria. Numerical experiments validate its efficacy, demonstrating robust performance in solving ill-posed problems. Furthermore, the method’s adaptability is showcased through applications to image restoration, highlighting its practical relevance.