Variational methods are commonly used to solve noise removal problems. In this paper, we presentan augmented Lagrangian-based approach that uses a discrete form of the L1-norm of the meancurvature of the graph of the image as a regularizer, discretization being achieved via a finite elementmethod. When a particular alternating direction method of multipliers is applied to the solutionof the resulting saddle-point problem, this solution reduces to an iterative sequential solution offour subproblems. These subproblems are solved using Newton’s method, the conjugate gradientmethod, and a partial solution variant of the cyclic reduction method. The approach considered herediffers 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,” andthe associated augmentation terms are all quadratic. In addition to the description of the solutionalgorithm, this paper contains the results of numerical experiments demonstrating the performanceof the novel method discussed here.
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