<p>High-order regularization models, especially those involving mean curvature, have gained significant prominence in variational image restoration due to their ability to mitigate the staircase effect and represent smooth intensity variations more accurately than first-order Total Variation models. Despite these advantages, the intrinsic high nonlinearity and non-smoothness of the mean curvature functional present formidable challenges for the development of efficient and stable numerical solvers. In this paper, we propose a novel computational framework for a class of mean-curvature-type models by integrating the Legendre–Fenchel transform within a primal–dual augmented Lagrangian formulation. By leveraging the duality properties of the Legendre–Fenchel transform, we reformulate the original nonlinear problem into a structured saddle-point problem. A distinguished feature of the proposed framework is its streamlined structure, which requires fewer auxiliary variables than traditional variable-splitting-based augmented Lagrangian methods. This reduction leads to enhanced computational efficiency and lower memory requirements. Numerical experiments on various image restoration tasks demonstrate that the proposed algorithm yields competitive performance in terms of both convergence speed and restoration quality, particularly in preserving geometric fidelity.</p>