The recovery of images from the observations that are degraded by a linearoperator and further corrupted by Poisson noise is an important task in modernimaging applications such as astronomical and biomedical ones. Gradient-basedregularizers involve the popular total variation semi-norm have become standardtechniques for Poisson image restoration due to its edge-preserving ability.Various efficient algorithms have been developed for solving the correspondingminimization problem with non-smooth regularization terms. In this paper,motivated by the idea of the alternating direction minimization algorithm andthe Newton's method with upper convergent rate, we further propose inexactalternating direction methods utilizing the proximal Hessian matrix informationof the objective function, in a way reminiscent of Newton descent methods.Besides, we also investigate the global convergence of the proposed algorithmsunder certain conditions. Finally, we illustrate that the proposed algorithmsoutperform the current state-of-the-art algorithms through numericalexperiments on Poisson image deblurring.
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