Fast Image Recovery Using Variable Splitting and Constrained Optimization

We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an 2 data-fidelity term and a nonsmooth regularizer. This formulation allows both wavelet-based (with orthogonal or frame-based representations) regularization or total-variation regularization. Our approach is based on a variable splitting to obtain an equivalent constrained optimization formulation, which is then addressed with an augmented Lagrangian method. The proposed algorithm is an instance of the so-called alternating direction method of multipliers, for which convergence has been proved. Experiments on a set of image restoration and reconstruction benchmark problems show that the proposed algorithm is faster than the current state of the art methods.

• Type: Journal
• Year: 2010
• Where: TIP
• Authors: Manya V. Afonso, José M. Bioucas-Dias, Mário A. T. Figueiredo
• Keywords: Augmented Lagrangian Method, Education, Image Restoration, TIP 2010, Unconstrained Optimization Problem