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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 33, Issue: 1, page 1-21
- ISSN: 0764-583X

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topIto, 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 -

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