Alternating split Bregman method for the bilaterally constrained image deblurring problem

This paper studies the image deblurring problem based on a bilateral constraint by convexly combining two classes of total-variation-type functionals. The proposed model including two L1L1-norm terms leads to some numerical difficulties, so we employ the alternating split Bregman method (ASB) to solve it which can be reinterpreted as Douglas–Rachford splitting applied to the dual problem. We also prove that the alternating split Bregman method owns the convergence rate O1M for the iteration MM. Experimental results demonstrate the viability and efficiency of the proposed model and algorithm to restore blurring and noisy images.