  We propose a new fast algorithm for solving one of the standard formulations
of frame-based image deconvolution: an unconstrained optimization problem,
involving an $\ell_2$ data-fidelity term and a non-smooth regularizer. Our
approach is based on using variable splitting to obtain an equivalent
constrained optimization formulation, which is then addressed with an augmented
Lagrangian method. The resulting algorithm efficiently uses a regularized
version of the Hessian of the data fidelity term, thus exploits second order
information. Experiments on a set of image deblurring benchmark problems show
that our algorithm is clearly faster than previous state-of-the-art methods.

Optimization and Control