Bound Alternative Direction Optimization for Image Deblurring

This paper proposes a new method, bound alternative direction method (BADM), to address the minimization problems in image deblurring. The approach is to first obtain a bound unconstrained problem through bounding the regularizer by a novel majorizer and then, based on a variable splitting, to reformulate the bound unconstrained problem into a constrained one, which is then addressed via an augmented Lagrangian method. The proposed algorithm actually combines the reweighted minimization method and the alternating direction method of multiples (ADMM) such that it succeeds in extending the application of ADMM to minimization problems. The conducted experimental studies demonstrate the superiority of the proposed algorithm for the synthesis minimization over the state-of-the-art algorithms for the synthesis minimization on image deblurring.