Titelaufnahme

Titel
Nonconvex TVq-models in image restoration: analysis and a trust-region regularizationbased superlinearly convergent solver
Verfasser/ VerfasserinHintermüller, Michael In der Gemeinsamen Normdatei der DNB nachschlagen ; Wu, Tao
Erschienen in
SIAM Journal on Imaging Sciences, Philadelphia, Pa., 2013, Jg. 6, H. 3, S. 1385-1415
ErschienenSIAM
Ausgabe
Publisher version
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (EN)image restoration / compressed sensing / nonconvex regularization / total variation / nonconvex programming / generalized Newton method / trust-region method / superlinear convergence
URNurn:nbn:at:at-ubg:3-707 Persistent Identifier (URN)
DOI10.1137/110854746 
Zugriffsbeschränkung
 Das Werk ist frei verfügbar
Dateien
Nonconvex TVq-models in image restoration: analysis and a trust-region regularizationbased superlinearly convergent solver [0.62 mb]
Links
Nachweis
Zusammenfassung (Englisch)

A nonconvex variational model is introduced which contains the q-"norm," q (0, 1), of the gradientof the underlying image in the regularization part together with a least squarestype datafidelity term which may depend on a possibly spatially dependent weighting parameter. Hence,the regularization term in this functional is a nonconvex compromise between the minimization ofthe support of the reconstruction and the classical convex total variation model. In the discretesetting, existence of a minimizer is proved, and a Newton-type solution algorithm is introduced andits global as well as local superlinear convergence toward a stationary point of a locally regularizedversion of the problem is established. The potential nonpositive definiteness of the Hessian of theobjective during the iteration is handled by a trust-regionbased regularization scheme. The performanceof the new algorithm is studied by means of a series of numerical tests. For the associatedinfinite dimensional model an existence result based on the weakly lower semicontinuous envelopeis established, and its relation to the original problem is discussed.

Notiz