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Variational methods are commonly used to solve noise removal problems. In this paper, we present an augmented Lagrangian-based approach that uses a discrete form of the -norm of the mean curvature of the graph of the image as a regularizer, discretization being achieved via a finite element method. When a particular alternating direction method of multipliers is applied to the solution of the resulting saddle-point problem, this solution reduces to an iterative sequential solution of four subproblems. These subproblems are solved using Newton’s method, the conjugate gradient method, and a partial solution variant of the cyclic reduction method. The approach considered here differs from existing augmented Lagrangian approaches for the solution of the same problem; indeed, the augmented Lagrangian functional we use here contains three Lagrange multipliers “only,” and the associated augmentation …