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Abstract This study proposes a nonlocal total variation restoration method to address multiplicative noise removal problems. The strictly convex, objective, nonlocal, total variation effectively utilizes prior information about the multiplicative noise and uses the maximum a posteriori estimator (MAP). An efficient iterative multivariable minimization algorithm is then designed to optimize our proposed model. Finally, we provide a rigorous convergence analysis of the alternating multivariable minimization iteration. The experimental results demonstrate that our proposed model outperforms other currently related models both in terms of evaluation indices and image visual quality.