Total variation regularization and fast algorithms based on alternating direction method

Total variation regularization is popular in image reconstruction due to its edge-preserving property. We propose an linearized alternating direction method to solving problems in image reconstruction with total variation regularization. The algorithm effectively combines an alternating direction technique to minimize the augmented Lagrangian function at each iteration. When the resulting subproblems do not have closed-form solutions, we propose to linearize these subproblems such that closed-form solutions of these linearized subproblems can be easily derived. Numerical results on image inpainting and image debluring show that the proposed algorithm is fast and efficient.