An active set strategy based on the augmented Lagrangian formulation for image restoration

Ito, Kazufumi, and Kunisch, Karl. "An active set strategy based on the augmented Lagrangian formulation for image restoration ." ESAIM: Mathematical Modelling and Numerical Analysis 33.1 (2010): 1-21. <http://eudml.org/doc/197600>.

@article{Ito2010,
abstract = { Lagrangian and augmented Lagrangian methods for nondifferentiable optimization problems that arise from the total bounded variation formulation of image restoration problems are analyzed. Conditional convergence of the Uzawa algorithm and unconditional convergence of the first order augmented Lagrangian schemes are discussed. A Newton type method based on an active set strategy defined by means of the dual variables is developed and analyzed. Numerical examples for blocky signals and images perturbed by very high noise are included. },
author = {Ito, Kazufumi, Kunisch, Karl},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {active set strategy; augmented Lagrangian formulation; image restoration; numerical examples; Hilbert spaces; convergence; Uzawa algorithm; Newton type method},
language = {eng},
month = {3},
number = {1},
pages = {1-21},
publisher = {EDP Sciences},
title = {An active set strategy based on the augmented Lagrangian formulation for image restoration },
url = {http://eudml.org/doc/197600},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Ito, Kazufumi
AU - Kunisch, Karl
TI - An active set strategy based on the augmented Lagrangian formulation for image restoration
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 1
SP - 1
EP - 21
AB - Lagrangian and augmented Lagrangian methods for nondifferentiable optimization problems that arise from the total bounded variation formulation of image restoration problems are analyzed. Conditional convergence of the Uzawa algorithm and unconditional convergence of the first order augmented Lagrangian schemes are discussed. A Newton type method based on an active set strategy defined by means of the dual variables is developed and analyzed. Numerical examples for blocky signals and images perturbed by very high noise are included.
LA - eng
KW - active set strategy; augmented Lagrangian formulation; image restoration; numerical examples; Hilbert spaces; convergence; Uzawa algorithm; Newton type method
UR - http://eudml.org/doc/197600
ER -