Kunrada KankamPapatsara InkrongPrasit Cholamjiak2025-07-072025-07-072025Rendiconti del Circolo Matematico di Palermo0009725X10.1007/s12215-024-01134-z2-s2.0-86000199199https://repository.dusit.ac.th/handle/123456789/7318The primary objective of this study is to establish the convergence theorem associated with the modified inertial projected forward–backward algorithm using line search techniques. Many applications in applied sciences can be modeled as constrained convex minimization problems. Our numerical experiments offer practical applications for resolving image deblurring issues. The results of our numerical analysis conclusively indicate that the proposed algorithms exhibit greater efficiency than those previously introduced in the literature. © The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature 2024.Constrained convex minimization problemImage recoveryProjected forward–backward methodArticleScopus