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Fast Image Recovery Using Variable Splitting and Constrained Optimization

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3 Author(s)
Afonso, M.V. ; Dept. of Electr. & Comput. Eng., Inst. Super. Tecnico, Lisbon, Portugal ; Bioucas-Dias, J.M. ; Figueiredo, M.A.T.

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.

Published in:

Image Processing, IEEE Transactions on  (Volume:19 ,  Issue: 9 )