Applying smoothing technique and semi-proximal ADMM for image deblurring

We present a new approach which combines smoothing technique and semi-proximal alternating direction method of multipliers for image deblurring. More specifically, in light of a nondifferentiable model, which is indeed of the hybrid model of total variation and Tikhonov regularization models, we consider a smoothing approximation to conquer the disadvantage of nonsmoothness. We employ four smoothing functions to approximate the hybrid model and build up a new model accordingly. It is then solved by semi-proximal alternating direction method of multipliers. The algorithm is shown globally convergent. Numerical experiments and comparisons affirm that our method is an efficient approach for image deblurring.