Fast Image Recovery Using Variable Splitting and Constrained Optimization

2010/04/09 by Manya V Afonso, Manya Afonso, José M. Bioucas‐Dias +3 · 12 citations
Computer Science · Engineering · #Image and Signal Denoising Methods #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques

paper · doi:10.1109/tip.2010.2047910

openalex publication_date 2010/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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.

Citations

• Multiplier and gradient methods
• A Tutorial on MM Algorithms
• Stable signal recovery from incomplete and inaccurate measurements
• Numerical optimization
• Compressed sensing

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