Result: An infeasible primal-dual algorithm for total bounded variation-based inf-convolution-type image restoration

Title:
An infeasible primal-dual algorithm for total bounded variation-based inf-convolution-type image restoration
Authors:
HINTERMÜLLER, M, STADLER, G
Source:
SIAM journal on scientific computing (Print). 28(1):1-23
Publisher Information:
Philadelphia, PA: Society for Industrial and Applied Mathematics, 2007.
Publication Year:
2007
Physical Description:
print, 34 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Calcul des variations et contrôle optimal, Calculus of variations and optimal control, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Programmation mathématique numérique, Numerical methods in mathematical programming, Sciences appliquees, Applied sciences, Telecommunications et theorie de l'information, Telecommunications and information theory, Théorie de l'information, du signal et des communications, Information, signal and communications theory, Traitement du signal, Signal processing, Traitement des images, Image processing, Algorithme, Algorithm, Algoritmo, Algèbre linéaire numérique, Numerical linear algebra, Algebra lineal numérica, Analyse numérique, Numerical analysis, Análisis numérico, Calcul scientifique, Scientific computation, Computación científica, Convolution, Convolución, Inversion matrice, Matrix inversion, Inversión matriz, Méthode directe, Direct method, Método directo, Méthode lissage, Smoothing methods, Méthode primale duale, Primal dual method, Método primal dual, Problème mal posé, Ill posed problem, Problema mal planteado, Restauration image, Image restoration, Restauración imagen, Donnée bruitée, Dualité Fenchel, Fenchel duality, Méthode type Newton généralisée, Generalized Newton-type method, Variation bornée, Variation totale, 49M29, 65K05, 94A08, generalized Newton-type methods, image restoration, total bounded variation
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
Department of Computational and Applied Mathematics-MS 134, Rice University, 6100 Main St, Houston, TX 77005, United States
Institut fur Mathematik und Wissenschaftliches Rechnen, Karl -Franzens -Universität Graz, Hein richstraße 36, 8010 Graz, Austria
ISSN:
1064-8275
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=18548972
Rights:
Copyright 2007 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics

Telecommunications and information theory
Accession Number:
edscal.18548972
Database:
PASCAL Archive

Further Information

In this paper, a primal-dual algorithm for total bounded variation (TV)-type image restoration is analyzed and tested. Analytically it turns out that employing a global Ls-regularization, with 1 < s < 2, in the dual problem results in a local smoothing of the TV-regularization term in the primal problem. The local smoothing can alternatively be obtained as the infimal convolution of the ℓr-norm, with r-1 + s-1 = 1, and a smooth function. In the case r = s = 2, this results in Gauss-TV-type image restoration. The globalized primal-dual algorithm introduced in this paper works with generalized derivatives, converges locally at a superlinear rate, and is stable with respect to noise in the data. In addition, it utilizes a projection technique which reduces the size of the linear system that has to be solved per iteration. A comprehensive numerical study ends the paper.