Bound Alternative Direction Optimization for Image Deblurring

This paper proposes a new method, bound alternative direction method (BADM), to address the ℓp  (p∈0,1) minimization problems in image deblurring. The approach is to first obtain a bound unconstrained problem through boundingthe ℓp 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 ℓ1 minimization method and the alternating direction method of multiples (ADMM) such that it succeeds in extending the application of ADMM to ℓp minimization problems. The conducted experimental studies demonstrate the superiority of the proposed algorithm for the synthesis ℓp minimization over the state-of-the-art algorithms for the synthesis ℓ1 minimization on image deblurring