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The problem of restoring images corrupted by Poisson noise is common in manyapplication fields and, because of its intrinsic ill posedness, it requiresregularization techniques for its solution. The effectiveness of suchtechniques depends on the value of the regularization parameter balancing datafidelity and regularity of the solution. Here we consider the Total GeneralizedVariation regularization introduced in [SIAM J. Imag. Sci, 3(3), 492-526,2010], which has demonstrated its ability of preserving sharp features as wellas smooth transition variations, and introduce an automatic strategy fordefining the value of the regularization parameter. We solve the correspondingoptimization problem by using a 3-block version of ADMM. Preliminary numericalexperiments support the proposed approach.

TGV-based restoration of Poissonian images with automatic estimation of the regularization parameter