  Although much research has been devoted to the problem of restoring
Poissonian images, namely in the fields of medical and astronomical imaging,
applying the state of the art regularizers (such as those based on wavelets or
total variation) to this class of images is still an open research front. This
paper proposes a new image deconvolution approach for images with Poisson
statistical models, with the following building blocks: (a) a standard
regularization/MAP criterion, combining the Poisson log-likelihood with a
regularizer (log-prior) is adopted; (b) the resulting optimization problem
(which is difficult, since it involves a non-quadratic and non-separable term
plus a non-smooth term) is transformed into an equivalent constrained problem,
via a variable splitting procedure; (c) this constrained problem is addressed
using an augmented Lagrangian framework. The effectiveness of the resulting
algorithm is illustrated in comparison with current state-of-the-art methods.
