Fast image recovery using variable splitting and constrained optimization

  • Authors:

  • Manya V. Afonso;José M. Bioucas-Dias;Mário A. T. Figueiredo

  • Affiliations:

  • Instituto de Telecomunicações and the Department of Electrical and Computer Engineering, Instituto Superior Técnico, Lisboa, Portugal;Instituto de Telecomunicações and the Department of Electrical and Computer Engineering, Instituto Superior Técnico, Lisboa, Portugal;Instituto de Telecomunicações and the Department of Electrical and Computer Engineering, Instituto Superior Técnico, Lisboa, Portugal

  • Venue:
  • IEEE Transactions on Image Processing
  • Year:
  • 2010

Quantified Score

Hi-index 0.01

Visualization

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.