  The problem of restoring images corrupted by Poisson noise is common in many
application fields and, because of its intrinsic ill posedness, it requires
regularization techniques for its solution. The effectiveness of such
techniques depends on the value of the regularization parameter balancing data
fidelity and regularity of the solution. Here we consider the Total Generalized
Variation regularization introduced in [SIAM J. Imag. Sci, 3(3), 492-526,
2010], which has demonstrated its ability of preserving sharp features as well
as smooth transition variations, and introduce an automatic strategy for
defining the value of the regularization parameter. We solve the corresponding
optimization problem by using a 3-block version of ADMM. Preliminary numerical
experiments support the proposed approach.
