Augmented lagrangian homotopy method for the regularization of total variation denoising problems

This paper presents a homotopy procedure which improves the solvability of mathematical programming problems arising from total variational methods for image denoising. The homotopy on the regularization parameter involves solving a sequence of equality-constrained optimization problems where the positive regularization parameter in each optimization problem is initially large and is reduced to zero. Newton's method is used to solve the optimization problems and numerical results are presented.