Fast Image Recovery Using Variable Splitting and Constrained Optimization

Details Fast Image Recovery Using Variable Splitting and Constrained Optimization Fast Image Recovery Using Variable Splitting and Constrained Optimization

2009-10-26

arxiv.org/abs/0910.4887v1

Mathematics

Optimization and Control

Submitted; 11 pages, 7 figures, 6 tables

Scientific paper

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 $\ell_2$ data-fidelity term and a non-smooth 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.

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