Bregman reweighted alternating minimization and its application to image deblurring

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In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the Bregman reweighted alternating minimization algorithm. The penalty parameter is set to increase in the iterations to speed up the algorithm. A convergence result is proved for the algorithm. If another smooth assumption is promised, with the semi-algebraic property, we can prove the algorithm globally converges to a critical point of the penalty objective function. Numerical results demonstrate the efficiency of the proposed algorithm.