title: Fast image recovery using variable splitting and constrained optimization.
abstract: 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 l2 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.
authors.affiliation: Instituto de Telecomunicações and the Department of Electrical and Computer Engineering, Instituto Superior Técnico, 1049-001 Lisboa, Portugal. mafonso@lx.it.pt
authors.forename: Manya V
authors.initials: MV
authors.lastname: Afonso
authors.forename: José M
authors.initials: JM
authors.lastname: Bioucas-Dias
authors.forename: Mário A T
authors.initials: MA
authors.lastname: Figueiredo