Augmented Lagrangian method for total generalized variation based Poissonian image restoration

Abstract

Instead of adopting the traditional total variation as a regularizer, this article introduces a second-order total generalized variation regularization scheme for deconvolving Poissonian image. Numerically, an efficient augmented Lagrangian method associated with alternating minimization method is described to obtain the optimal solution recursively. In addition, we provide the rigorous convergence analysis for the resulting algorithm at great length. Finally, compared with the total variation based efficient strategies, numerical simulations definitely indicate the competitive performance of our proposed approach to deblurring poissonian image, both in terms of restoration accuracy and edge-preserving ability.